The integration between smartthings and Alexa exposes smartthings controlled devices to Alexa but not the other way around. So those Bluetooth devices will not show up as Devices in smartthings unless they have their own separate smartthings Integration.
You can get a partial integration by using an Alexa routine and a smartthings virtual sensor so that when the virtual Sensor opens, you can have the Alexa routine turn on the zimi Switch. But it’s still only one way. If you turn on the zimi switch in any other way, including via voice control to Alexa, SmartThings won’t know it was turned on.
Whether that’s useful to you or not, just depends on the details of what you are trying to accomplish. 
There are many devices that fall into this situation. They work with Alexa or Google assistant but not with smartthings.
It’s possible that the new “matter“ standard being introduced will help with this and more devices will become compatible with each other, but that will likely be early next year at the soonest and won’t cover all devices, just those where the manufacturer has decided to add matter compatibility.
Here’s the FAQ on setting up the integration if you do want to try it: