I know I’ve done it without any problems (other than the process of mapping the USB drive taking a little while to figure out), but unfortunately that was on my old laptop and a couple of years ago so I don’t have exact version numbers handy.
Some version of Ubuntu LTS (could have been 12.04 or 14.04, don’t remember) and I used the Play on Linux GUI to set up Wine and launch the installer exe. Not sure what version of Wine but it definitely wouldn’t have been anything right on the bleeding edge, even for the time.
Does it need to be Ubuntu 16.04 LTS in particular or is switching to a different distro an option?