[@Atrophy] *judges silently*

If the door is closed he will go through it.  While in the current dimension, the door is closed and will stop physical interaction, when Cyrus reactivates Hike! he ascends up to an iteration of the fourth dimension.  So I'd imagine he'd be able to go through the door as if it were still open.  (Though if he goes through a door, someone closes said door, and if he tries to return to a snap shot that's now within the closed door, I don't imagine the final few seconds of his life to be very pleasant at all.

For the Hike! I don't think so.  In my mind, Hike! will pull him back quick (I'm thinking for every five seconds under the spell, the return trip might be one second)  The second form, Break!, is pretty much instantaneous.