Yes, it's possible. In fact, there are many people who fell for such scam tactics.
But what they actually they do are modifying unencrypted part of the wallet.dat to show address which doesn't have it's private key pair.
Is there any way to find this?
Aside from suspicious people who sell/give wallet.dat contains Bitcoin, there's no way to determine whether a wallet is "fake wallet" without decrypt the wallet itself.
Thread mentioned by @jseverson will tell you more about it.