No, this is not how fullmatch() works. Otherwise there wouldn't be need to add it into the stdlib. You could just check end() of the result.

fullmatch() acts like match() with added \Z. But if the pattern contains multiple alternates you need to add \Z at the end of every branch (r"foo\Z|bar\Z") or wrap the entire patch in a non-capturing group (r"(?:foo|bar)\Z").