Good question. Probably had a better chance 6 or 7 years ago when Internet gaming was still in it's infancy and everything was run much more haphazardly then it is now.
Since automatic shuffling is the norm after every hand, any advantage you can gain by card counting is negated. To make counting work, you would need to find a game where shuffling isn't done after every game, and where the decks used are allowed to run their course. This may be impossible to find, but if you did find such a game there would be potential.
Since shuffling is done after every hand, the only way I can imagine getting an advantage would be to find a one or two deck game and to play every spot on the table, then you would know what other cards have been dealt and could get an advantage, as you could potentially see half the deck when playing at third base. Again, probably not going to find such a game, but theoritically it's possible.
For those knocking your question as idiotic probably don't have a firm understanding of the game and the potential advantage one get get by card counting. Keep in mind that Vegas was dealing a beatable game for 50 years before Edwin Thorpe figured out how to beat it in 1961. So the possibility that an on-line casino could offer a beatable game is certainly possible, but unfortunately unlikely.
And lastly, one should not forget that advantages of bonuses, and I wouldn't be shocked if there were some players out there that can get an advantage by combining perfect strategy with various promotions that are offered. Keep in mind that the edge in a 6- deck game of blackjack with favorable rules is less then .3%, so coupling perfect play with bonses can very easily result in a positive expectation.