This post contains some spoilers of Fallout 4 storyline, so if you wish to avoid those, stop reading this.
Although the following is based on some facts gathered from gameplay, this is all still purely speculative and personal opinions, YMMV, consider this just some food for thought..
My take on this question is that it is indeed a fairly likely possibility at least that the Sole Survivor is a synth (Gen 3 newer) - This is never conclusively confirmed or denied in game, but the Sole Survivor secretly/unknowingly being a synth would indeed make certain kind of sense.
In the beginning of the game, vault 111 cryopod lifesupport system is down and everyone who remained in the cryopods for the last freezing cycle is dead - Same pipes run into all of the pods, but miraculously somehow only the Sole Survivors pod is still perfectly functional and she/he revives with ease.. This scenario does give a very long window of opportunity to replace the Sole Survivor with a synth, presumably with uploaded memories of the original. In this decades long timeframe, it would be entirely possible to replace the entire cryopod with a specially made functional one, even to keep all of that secret from the institute at large.
Who would replace the dead Sole Survivor with a synth? .. the Father, wanting to run a secret personal experiment for mostly personal motives and reasons. Rest of the institute would not have been told of the replacement synth at all, for obvious reasons. If Father can indeed keep secrets like the whole FEV Human Experimentation Department under wraps from some of his own department heads, secretly pulling off an unregistered synth replacement and even a cryopod installation in Vault 111 (a remote location) would be easy.
Further evidence I was able to find in game was what seemed like false or corrupted memories from before the freeze - In pre-war Sanctuary Hills the Sole Survivor remembers from the time right before the bombs (experienced while running to the vault), there are no white picket fences to be seen anywhere - Yet, after emerging from the Vault 111 and returning to the postapoc Sanctuary Hills, every house is surrounded by damaged white picket fences.. The way I see it, this kind of error might occur if a synth mind is read frex from a damaged, dead brain of a human corpsicle - Maybe some of the missing memories had to be artificially recreated, and the person doing the mindjob made some mistakes.. Later on in the game, when talking to Daisy in Goodneighbor the false memory of non-picket-fenced Sanctuary Hills is directly contradicted by the Sole Survivor telling about his/her pre-war house having white picket fences.
(Note: The missing white fences in pre-war Sanctuary Hills could of course also be a game design bug, but it is a bit strange how it was never fixed in any of the official updates for the game. Perhaps it is intentional.)
Also worth mentioning, never any weight gain or other ill effects for seriously overeating for the Sole Survivor, even with the Survival Mode active. (This is a Gen 3+ Synth feature, they never gain any weight due overeating, like a human would.)