I would think the odds are slim to none. Highly doubtful it could latch on while you are swallowing. Once inside the acidic environment of the stomach it wouldn't last long there either.
Did you swallow a tick? The lining of the esphoagus is well lubricate with saliva among other things. It would need time to embed itself in the lining and start to suck.
I'm going with no, since it's like asking can you win the powerball lottery, while fucking Jessica Biel, getting struck by lightning, which renders you impotent, but does nothing to Biel, on a sunny Wednesday at noon with no clouds in the sky.