GUI fuzzing is a thing, yes. I've seen it mostly on mobile apps but I'm sure you have it for other type of GUIs.
Example of tools: https://www.fuzzingbook.org/html/GUIFuzzer.html
GUI fuzzing was a thing way back on the original Macintosh: https://www.folklore.org/StoryView.py?project=Macintosh&stor...
Something similar should be reasonably easy to build these days using AutoHotKey or the like. I bet it's been done.
Fuzzing is a pretty popular testing technique for libraries, but GUI software has not seen the same attention.