Normally, yes, you can go through the ped gates and cycle in there anytime. However, during the twice yearly deer cull, the gates shut at 8pm. The culls go on for approx 6 weeks, the current one started on 1st Feb, so is probably still ongoing but I haven't been in since Saturday and didn't take note of the signs.
You'll still be OK until 8pm but make sure you will reach your exit by then.