Yes, and it's not a problem. The security requirements for micro-transactions are not as high, so using payment processors or p2p micro-banks would be fine.
In fact, it has the advantage of being much faster. Your savings would still be safely in your own hands, and if tx volume at any given time is small compared to the cost to gain peoples' trust, micro-transaction fraud yields no profit.
Exactly. We already have examples of these p2p micro-banks. Most of us already use them without knowing it. Mt. Gox is a p2p micro-bank that offers the ability to transact micro-payments with no fee, using their redeemable codes (denominated in BTCs, USDs, EURs, GBPs, etc.). These redeemable codes / vouchers / coupons etc are today offered by many exchanges (Bitstamp. CryptoXChange, Bitcoin-24, and more) and now some eWallets are introducing them (e.g. EasyWallet.org) so there is already a method for a service to use bitcoin for micropayments where there are either no fees or the frees are ridiculously low (compared to any other alternatives).
Additonally, each service that has its own EWallet is internally able to support bitcoin-denominated micropayments without a fee for its users. Ogrr.com is a great example of how this is done today.
Also, each micropayment doesn't need to be an individual transaction on the blockchain. The transaction fee can be shared among multiple transactions, lowering the per-transaction code. This is how the Bitcoin Faucet works, for instance, when it hands out its pennies-worth of transactions throughout the day.
So eventually it probably won't be feasible for microtransactions themselves to cross the blockchain. Once that day arrives there are already alternative approaches that work nearly as well. In the meantime, there are services like SatoshiDICE and others that have the opportunity to take advantage of this period where ultra low cost microtransactions that cross the blockchain are possible, and build a customer base while following a strategy that is compatible once the day that the "nearly free, ultra low cost" feature goes away.
Though there is a wide gap between fees that are "free or nearly free" and those that are "multiples of pennies" per transaction, the difference means little to most every normal commercial and P2P transaction so this issue is isolated solely to the use of microtransactions that themselves are amounts measured in pennies.