At most, you might need to do some procedures during your internship Neuro/IM rotations, but psych residents are generally not expected to do intubations, central lines, etc. after internship.
As a psych intern, a patient on our team needed a paracentesis, so they offered to let me do it. I didn't even pretend to be interested 🙂 (however, I had a very chill team that month who totally understood - I wouldn't recommend taking that approach with just anyone).