SZF,
Officially, no I don't think it is allowed at non-ATC airfields. Unofficially, if both of you are on the radio, and you know the other guy's call-sign (which you would do if you've been listening to his radio calls) it's not completely unheard of to ask him if he minds you going inside him. I've been passed like this several times, and have also passed other pilots like this several times. As long as there's good communication and everyone has everyone else in sight, it's not a problem. Generally tends to happen more often on the crosswind-to-downwind turn than anywhere else when a faster aircraft is behind a slower aircraft, in my experience.
FFF
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