We don't really get a chance to be replaced, I think, unless they stuck the synth player back into the cryo stasis pod, or replaced him at the Institute itself after infiltrating it. However, the ending if you side with the Institute makes me think that this isn't really true.

Dogmeat, on the other hand, is totally a synth. The Institute seems to have a habit of making synths out of extinct species/breeds of animals.