I'm sure they've changed this multiple times. My understanding is they used to basically put you in a 'loser' bracket where you wouldn't get as good of matches (or just get matches with other people doing the same thing). You wouldn't get banned, but you also wouldn't get the best matches.
EDIT: Note this is on Tinder. Don't know if Hinge is any different...
The Hinge API doesn't explicitly track your "desirability" bucket, but JSwipe (Tinder for Jews) does. I was curious how their API compared, and there's a field which records the percentage of users who liked your profile.
After doing this for a week, it does seem like the quality of my suggestions decreased, but they returned to normal if I limited the number of automated swipes.
TL;DR: automating up to ~20 swipes per day is the sweet spot to maintain match quality.
EDIT: Note this is on Tinder. Don't know if Hinge is any different...