In theory, yes you should be able to do that. I'm not sure if you will be able to integrate with existing wallets, or if you will need to create your own wallet app however. Many popular wallets have not yet implemented account abstraction, so we are not sure yet what kinds of tooling we will get for integrating with things like say metamask. That's something I guess we will have to wait and see.
But if you were to create your own wallet provider that integrates with walletconnect it would connect to most sites. Then build your transactions to use eip 4337 with your paymaster, and it would work.
Maybe you could also try and make a wrapper around like metamask or something, but I'm not sure how that would work.
In order for users to be using your service, they will need a 4337 wallet setup somehow. You would either need to integrate with a wallet provider that supports 4337 wallets, or create your own, in theory. Because you need to inject your paymaster into the transaction creation, since in 4337 the paymaster information is submitted with the transaction when it goes to get verified on chain.