There are no inherent restrictions on entering time - your project and task timesheet filters drive everything.
Your timesheet filters define which projects and tasks are eligible for time tracking. If, for example, you do not want any time charged to a closed project, you would include "Status is Implied Open" in your project timesheet filter. Alternatively, you can use a condition like: Project Dates Overlap with Timesheet Period is equal to "Yes".
The benefit of using timesheet filters is they allow you to configure a grace period. Use the "Number of days to extend timesheet start and end dates" timesheet setting to give your users a little more leeway to enter time once the timesheet "close" condition is met. For example, if you use "project and timesheet dates overlap" you can use this setting to give your users a few extra days to enter time once the dates cease to overlap (then the PM doesn't have to adjust the project dates to open up the timesheet for stragglers).
If you use the project timesheet filter "open projects," then dates do not matter as long as the project has an implied project status = open.
If you use the filter to "project and timesheet dates overlap," then status doesn't matter. You could charge time to a closed project as long as the dates overlap - even if there is a completion date (that is the future). Entering a completion date will change the "end date" of the project, for example: project dates are 6/1/16 to 12/31/16. If you enter a completion date of 9/1/16, you'll be able to charge time from 6/1/16 to 9/1/16.