If a dapp has a built-in wallet, can the users intearact with the dapp without the need of Metamask or Mist?
I'm not 100% sure what "wallet" means, in this context, since the term is rather poorly defined.
That said, the function that MetaMask and Mist play is to hold the user's private key and thus protect them from having to share it with a DApp. If your DApp holds the user's private key for some reason (because it's a "wallet?"), then a user would not benefit from using MetaMask or Mist.