Effectively you're just using your server to implement a payment cache. It accumulates the micro-transactions, then every time they reach (say) one bitcoin for a user, that transaction gets flushed out to the real bitcoin network. The same thing going the other way, a bitcoin comes in to the payment cache, and that coin gets nibbled away at until it's gone.

Of course this is just another way of thinking about an "account" system. But it shows that you're not "turning" the bitcoin system into anything.