Really the only real issue is brittle filament (PLA-CF) tends to cause jams. There’s the abrasion on the PTFE tubes, so you’ll have to replace them sooner. Really that’s it.
I use ABS-GF quite a bit, using it right now. Haven’t had any issues, and I suspect you wouldn’t with ASA. Would love to have some BL ASA-GF at some point.
You’ll be fine. Just keep brittle and PTFE tubes in mind. I’d get some spares.
Another thing to toughen up are those funnels in the AMS where the filament enters the mechanisms. Look for “AMS saver” on MW. They use various approaches to keep filament from rubbing grooves in the funnels.
I’ve been using PC-CF in the AMS for a while now with no visible damage. I always use the same slot in the same AMS so if it is slowly destroying it I can contain the damage lol. Now I have one roll of PA6-CF that actually worried me because it feels like sand paper to the touch. I actually move the AMS forward and use a homemade filament roller behind it so it goes directly in the printer.
I just bought a spool of the ASA-GF which the website lists as AMS compatible. When I loaded it into the AMS is recognized it and indicated the correct color and a full spool. Then after a few seconds that slot was cleared and ? was shown. When I manually edited the filament, it popped up a warning that CF filaments are brittle and can cause problems in the AMS. So which is it? Is it AMS compatible or not? I assume the firmware (which is latest) thinks not which is why it clears after correctly recognizing it.