If I were to pause my emulator in the middle of the run, would that invalidate the run? Sometimes I have issues with my controller and I can't properly pause the game. If I'm doing 105% for instance, it's pretty likely that something will happen to my controller, since the category is longer.

Am I allowed to pause the emulator and resume when i get my controller issue fixed?

I don't think it should be an issue. I used to run Crash 2 on emulator and if I accidentally paused the emulator in the middle of a run or if I had to fix my controller I would just fix the issue and accept the timeloss.

You can pause the emulator as much as you want, but not the timer.