The update is made for the physical 68K based real Amiga machines, so that is what we promise where it works. No promises for the MiST, of course, but it would astonish me if it would not work.
It comes with its installation script that performs a clear install. Even though this is the recommended way of installation, you will then get a workbench that looks exactly like the 3.1 workbench.
Just tried it on my MiST running Minimig-Mist 1.2.3 Beta and it seems to work fine. I was able to boot both from the ADF and from a 4 GB .HDF which I had prepared in WinUAE.
When adding BestWB to the install, it crashes on the next boot (on the MiST but not in WinUAE). "Software Failure - ramlib #80000004". However that's not related to OS 3.1.4 itself of course, since that's a third party modification. I'm guessing it's adding something to the startup-sequence, Devs: or somewhere that's not compatible. Will have a look later.
Edit: Turns out the problem was 68020.library that BestWB installs. Removed that and it works great now. So if any of the other 5 people who own a MiST want to try it, that's what you have to do
