Do you agree with the concept of timelines starting at different times.
Well, on the infinite universes theory, anything could be happening, including an identical development to ours just (say) five years later.
I
think the concept of the parallel universe is that we are all at the same point in time (without other intereference, anyway) from some universal start (e.g. big bang), just at different points in space/reality. So, travelling across realities should get people to the same point in "time", as shown when using the mirror in series 3.
So, in answer to your question, I would guess we could, but only because of the possibilities, not on the original principle.
The question comes down to, if the mirror allows trans-reality jumps, does it always reproduce itself into that reality, or does it rely on already existing in that reality, to connect to?
Thinking about what I said, although it would beautifully answer the question of how it got to P3R-233 in the alternate reality, there is a massive drawback. As Apophis (alternate) found out, having the mirror simply appear in any reality where the "viewer" is looking is a security nightmare, since people could come in, but without the remote control to turn it on, you could not go to them.