Not properly.
Just wait till all the Advantage Players hear about this
There is a big difference between allowing free play without registration and only asking for details once a depositing player wins.
What about a player who never manages to withdraw. He could play for months before you get hit by a massive chargeback because the whole thing was a fraud, and the CC company has just gotten around to dealing with it. Worse still, he may have found a way to get the money through your systems and out via another account, rather than withdrawing it. ANY game where it's player vs player, or even a multi player single dealer game, can be vulnerable to collusion.
At the latest, details should be gathered at the point where the player tries to make their first real money deposit.
If you rely on the details of the deposit method for determining who is playing, you are verifying the account, not who happens to be using it to deposit at the casino.