If a soul can be imbued into an object, could it be placed into a soulless body from within a soul gem?

Maybe. At least, some Redguards seem to think it's possible since they tried with Prince A'tor (in the game Redguard).

In Redguard, there was a attempt to do just that with the soul of Crown Prince A'tor, but the soul wound up in his sword instead. Actually hard to say if such a thing is possible, as the attempt seems to suggest that the idea is achievable, but there's no actual record as of the moment of it actually working.

Actually, there isn't as far as I'm aware an instance of bringing the long dead back to life unless they were already involved with the arcane or some deity.

Zurin Arctus used the matella to trap Ysmir. Of course he got killed as well, and they along with Tiber Septim mantled Lorkhan and became Talos. But before old Hjalti dies he used the mantella to power the numidium. I know the numidium isn't human, but that's about the closest example I can think of. We also get to see Malyn Varen's soul inside Azura's star, and you had to kill him to get it out. Perhaps death is the only exit from a soul gem?

Well, you can get partially soul trapped in Dawnguard and then reclaim your soul, so I imagine that it might be possible.

@SneakyMammoth: But your soul was also in there, so that would suggest that, at least as far as Azura's Star is concerned, if the soul in the Star and the wielder are both in agreement, the soul can be removed from the Star. But that might also require a still living body. Most Soul Traps are triggered by death.

The Vampirism Cure in Skyrim requires a filled Black Soul Gem. I have not used the Vanilla Vapirism Cure from Oblivion, but I think it also required Soul Gems. In Morrowind the "Cure" was produced by Vaermina and aquired by Molag Bal after fulfilling a Quest for Him.

I believe that Arkay actually interferes with the placing of a Soul that has been removed from a Body by Death back into the Body.

In a Daedric Realm I think it is completely possible.

A sufficiently talented individual might be able to accomplish this. Aside from the Prince A'tor example, we also have Calixto in Skyrim. Admittedly he wasn't going to put Lucilla's soul back into her body (probably wasn't fit for purpose) but that avenue of magic might be useful to attempt such a thing as the OP's question.