In fact, I just did try it out: searching for the ligature "fi" in Firefox (on Linux) does not find "fi". Neither does it work the other way around.
This suggests some questions.
1. Are fi.com and fi.com the same as far as DNS in concerned, or could both exist as separate websites?
2. If they are separate websites, do the various password manager browser extensions recognize they are different, or might they fill in your fi.com password when you are getting phished with fi.com? Same question for the various browser's built-in password and form savers.