If you want to calk the gap between the dry wall and the floor using caulk backer rod seems like a good idea, it's a closed cell foam that you pack in to large gaps then run a bead of caulk over, they allow the caulk to be thinner so it can flex instead of cracking or separating.
As for caulking the vapor barrier to the dry wall, that is going to allow moisture to wick up from the floor in to the dry wall, calking it right to the floor using a polyurethane caulk.
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