If we assume these caveats then is it fair to say that colliding branes requires concepts like "space" and "time" to exist in a multi-brane-verse?
It's not just fair to say, it has to be the case. Our spatial dimensions are just a subset of those of the higher "brane-space", and we inherit the time dimension.
If so what does this tell us about the generality of concepts like time and space as applied to entities that are not our universe?
I would be very careful about any "generalities" - each specific model or hypothesis carries with it its own specific structure. Remember that these models are born out of the mathematics, not the other way round. The apparent vagueness of the terms bandied around in such discussions is purely a function of their layman presentation. This is in stark contrast to pseudo-science bullshit, where the vagueness is an inherent property of the "model".