The phone could simply hold the private keys and be able to sign transactions that the server generated for it after displaying it to the user for confirmation. This would require very little resources such as CPU or bandwidth.
This is a great idea, I have family in other countries and it is so expensive to send money.
Mpesa is used by millions in everyday transactions, bitcoin could steal that market no problem with its low fees.
Bitcoin as a replacement for Western Union is an awesome idea. But more than likely this is going to spring up because there are service providers (ie. internet cafes) that start offering the community lower rates than Western Union can do. In this case Bitcoin will likely just be the transport mechanism (ie. EUR -> BTC -> THB), not that the end recipient actually desires to hold bitcoin.