Unfortunately, It probably won’t work the way you are imagining. The smartthings hub has two different radios in it, one for Z wave and one for zigbee. The only thing that ties the two together is your SmartThings cloud account.
The Z wave radio in the smartthings hub is a certified Z wave controller, so technically it can be added as a secondary controller to another Z wave network. However, this doesn’t bring the zigbee devices with it, and those would continue to be completely invisible to your HASS setup.
Moreover, the SmartThings hub expects to be the primary Z wave controller, so much so that SmartThings officially won’t support its use as a secondary.
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.
And if you go ahead and do it, the SmartThings hub lacks some of the utilities that would allow it to work smoothly as a secondary Z wave controller. You may find that statuses are not communicated between the two controllers. And if you add new zwave devices, you may have to completely remove the SmartThings hub from your HASS network and then re-add it again from scratch or the new devices don’t show up.
There are some people who do have SmartThings successfully working as a secondary Z wave controller for some very specific use cases. But there are probably more people who have tried it and then abandoned the effort because they didn’t get the results they wanted.
So you can try it and see how it goes, but you need to be prepared to completely rebuild your SmartThings network if it doesn’t work. And you won’t get any control of your zigbee devices in your HASS system. It’s only the Z wave devices that can be shared, and even then, the statuses may get out of sync. And SmartThings support will not help you with anything if something goes wrong because of their “strongly discourage” statement above.
You can search the forums for “secondary controller” and find discussions of what people have tried, but I think using MQTT to bridge the two is likely to be a smoother integration for you.