The Z wave standard allows for the possibility of multiple controllers on one network, but one controller is the primary and any others are “secondary.”
(also, for the purposes of this note, I’m going to assume that you meant “Openhab,” a popular open source platform often used with Z wave devices.
If by chance you meant something else, we would need to know more about that particular platform.)
A. SmartThings as a Primary Zwave Controller
So far, so good. the problem is that while the SmartThings hub does contain a certified Z wave controller, it is a multiprotocol platform, and of course most of your processing runs in the SmartThings cloud, and so it just doesn’t play nice with other zwave controllers.
If SmartThings is set up as the primary Z wave controller, You can add another controller device like an Aeotec USB stick running on a laptop, and have that other device be a “secondary.” But only for Z wave. And SmartThings does not support all of the advanced zwave options for controller management, like controller shift.
All of which means that your secondary has to be smart enough to continually request new information from the primary, and also you can’t switch back-and-forth between which one is the primary, which is something we do for some use cases.
use case 1: SmartThings talks to the secondary, and the secondary is part of a platform which can talk to some end devices which are invisible to smartthings
So what would you get from having another Z wave controller on your network acting as a secondary?
It really comes down to specific use cases. Most commonly if the other controller is part of a system which happens to have additional protocols that SmartThings doesn’t have, you might use it so that you would have a total system where your Z wave devices could act as proxies, like virtual devices, and you could get some control from SmartThings over some of the other protocol devices that way.
For example, openhab works with EnOcean Devices if you have the right plug-ins and antennas. Smartthings does not have any way of talking to enocean devices.
So if you had a group of switches in one room and four of them were Enocean and one of them was Z wave, and you always wanted to treat them all as one group, it would likely be possible to add a Z wave controller that works with openhab and have that controller be a secondary to your smartthings hub and add just the Z wave switch to SmartThings and then when you turned on that Z wave switch from SmartThings, openhab would also turn on the Enocean switches.
You would never actually see the Enocean switches as things in your SmartThings account, but you could set up some automations where the end result would be those switches going on and off.
We do have some community members who have done stuff like that with both vera and with the staples hub.
The main problem is that because SmartThings doesn’t support all of the advanced controller options, it can get very annoying as you start adding additional Z wave devices. In some cases you will have to completely remove the secondary and then completely re-add it in order to get the new device information.
But it is an option that works for some people in some situations.
use case 2: using utilities that the secondary controller has that smartthings does not
For reasons that have never been fully explain, but that probably go back to that multiprotocol issue, smartthings does not provide customer-facing network mapping utilities for its Z wave network. But if you add a secondary, most commonly an Aeotec zstick, you can use the secondary’s mapping utilities to see your entire Z wave network. There are community members who have added a secondary just for this purpose. 
Use case 3: run the secondary locally if the internet is down?
To be honest, I have no idea if the secondary Z wave controller can continue to operate locally if the SmartThings cloud is not available to the smartthings hub acting as the primary zwave controller.
Theoretically, I would think that it would. Just as a Z wave direct association will work even if the SmartThings cloud is not available.
But I have learned with SmartThings not to assume that reality will follow theory. 
I have not heard one way or another from anyone who has this kind of set up whether their zwave network from a secondary controller continues to operate fine if the SmartThings cloud is not available. Hopefully someone who has tried it can let us know.
So all I can say at this point is that it’s possible it might work, but someone would have to try it to know for sure.
Conclusion: SmartThings as zwave primary, OpenHab as zwave secondary
So you could have SmartThings as your Z wave primary controller and openhab running an Aeotec zstick on a laptop as your Z wave secondary controller and both would have access to the Z wave devices that were connected to SmartThings at the time that you added the zstick to your network as long as the SmartThings hub was running as expected.
You can’t run the openhab software on the SmartThings hub itself. You have to get a completely separate Z wave controller Device, again, most typically the Aeotec zstick, and then add that device as a secondary to your SmartThings Z wave network.
As far as what you would get out of that, some additional utilities and maybe the ability to do some indirect integration with some devices of other protocols.
What I don’t know is whether you can get any additional local operation that way. I know that custom code device type handlers would not be available if the cloud is not available, because they are not loaded into the SmartThings hub itself. So I have no idea how the secondary Controller Will work if the primary can’t reach the cloud. Again, I hope someone who has tried it and tell us more.
B. OpenHab as primary, SmartThings as secondary
Smartthings cloud architecture just doesn’t make this work well. In fact, SmartThings now has an official support statement that says they will not help you if you try to use the hub as a secondary, which is never a good sign. 
SmartThings strongly discourages adding the Hub to another Z-Wave network. We cannot offer support for disconnected Z-Wave devices or the inability to add devices through the Hub as a result of including the Hub into another Z-Wave network.
I know there are a few community members who have added a SmartThings hub as a secondary, most typically to a security system, but they are only using it for pretty simple stuff, usually control of lights, and in general I think this is not going to work as expected.
Sorry that answer is so long. The multiprotocol aspects of the SmartThings platform, and in particular, the cloud-based architecture, just really complicates this issue.
If you want to try it, you should try adding your openhab device as a secondary, and see what happens. But the results may not be satisfactory, and you should be prepared to completely rebuild your openhab network from scratch if necessary. Maybe even a couple of times. So it’s not going to be a smooth or easy set up.