Thanks to a transportation issue, I was nearly 15 minutes late for a POTC FP+ in December. We were worried about being late, so we said something to the CM and he told me to try the band to see what happened. When we got the Green Mickey without the CM doing anything, the CM said, "You had 37 seconds to go." We were just a couple of minutes late for a TOT FP+ in August, and we got the Green Mickey with no CM involvement.
We also showed up about 30 minutes early for a Peter Pan FP+ by accident, and when we got the Blue Mickey and realized our mistake we told the CM we'd come back during our actual window, and he basically said not to worry about it and overrode the system for us and let us into the line.
Based on these experiences, I think there are definitely automatic grace periods built into the system. I also can't imagine a CM overriding a Green Mickey and denying entry if you are within one of the automatic grace periods. That would be a pretty jerk move.