Will Winebottler work with licences?
Generally Winebottler can handle licenses, but it works simulating the Windows API, so you have to fine tuning some components and DLL if something is implemented using non common Windows API / DLL, which it means that sometime license verification is implemented with esoteric business logic and may require some particular DLL which doesn't run well with the emulator. 

In conclusion, I think that you have a good rate of success because your program is also running as limited edition, and I don't think that it could be a problem to have a test, at least it doesn't works and you can always uninstall it and recover your license key.

As far as I know usually licenses are provided per user or per machine. If you uninstall the software from your emulator you still have you license ready for another installation, maybe using virtualization software like VirtualBox or a Windows dedicated partition baked with BootCamp.