nothing will happen. i've been doing it since adobe changed from cs6 to the first cc version years ago.
it's not unusual for me to develop an application using adobe animate on my pc and on my macbook concurrently.
furthermore when i would go to my office and try an open an adobe program, i would be prompted to sign out of one of the two home computers, so i could sign in on my office computer and use my adobe programs. upon returning home, i would be prompted and sign out of my office computer to use both home computers etc.
and swaying to the philosophical (and possibly ridiculous side) i'm not actually using both home computers at the same instant. ie, i don't find it practical to even click a program option on both home computers at the same exact instant, even though they are side-by-side and i'm ambidextrous.