Do U.S. aircraft carriers still include a Marine Corps squadron?
According to Wikipedia's page on Carrier Air Wings, there are nine active carrier air wings currently active (for eleven aircraft carriers).  Of those nine, CVW-9 includes Marine Corps squadron VMFA-314 operating the F-35C Lightning II, and CVW-17 includes VMFA-323, which operates the F/A-18C Hornet.
So out of nine carrier air wings, two include Marine Corps squadrons.  Not all carrier air wings include Marine Corps squadrons.  I believe other Marine Corps squadrons train on aircraft carriers, but are not permanently associated with air wings like VMFA-312 and VMFA-323 are.