If there are other universes, would they be detectable from within ours?

No, because our universe according to general relativity represents everything that emerged from our Big Bang, and includes galaxies and space beyond our visible universe. Other universes represent completely different space-times that are outside our own spacetime completely. They do not now, or ever will in the future, have any physical contact with ours, and are thoroughly beyond observation even when the universe we are in becomes infinite after an eternity of time. These universes are literally on the other side of eternity and infinity from our perspective!

But some cosmologists expect that there could be a measurable effect upon our visible universe from matter just beyond our visible horizon. These 'super-horizon' influences would cause a slight alteration in the cosmic background radiation at its largest angular scales.