I've used vanity miner before, and I've tried guessing an existing address, but according do vanitygen, it takes more than a billion years on average to solve. Assuming I was lucky enough to mine the exact same address, could I get the privkey?
Yes, in theory. Note however that you provided the actual answer yourself: The chance is so vanishingly small that it is, for all practical purposes, simply impossible.
If there isn't some RNG collision... I had experience with one same address in btc core and on blockchain.info Probably got so lucky=) No import\export of course. Generated with period 1 month+. This year. When developing exchange of BitMoney. No proofs but it happened.
So...
P.S. Oh i see there was some bug on blockchain.info, but how it could coicide with btc core?