The official policy is that time windows are strictly enforced. I've haven't read about many folks being successful able to use them early (even just a few minutes), but it's more common to hear about the 15 minute grace period or even far beyond the window. The short answer about using them later is "maybe" but don't count on it.
I would do everything possible to get there during the one hour time window, but if you are running a few minutes late, it doesn't hurt to try. I think you stand a pretty good chance of getting in if you're less than 5 minutes late because everyone's watch runs a little differently (even the clocks on Main Street and the Castle aren't always in sync!). However, I do think it's up to the CM at the FP entrance and it probably depends on whether they stick to the rules, how busy the FP line already is, etc. You can't count on there being a grace period, but it doesn't really hurt to ask either (especially if you're only a few minutes late).