There are things that the third world already uses for this purpose, such as M-Pesa. Money through SMS is already in wide use, for millions, right now. How can I send someone bitcoin through text messaging? http://en.wikipedia.org/wiki/M-Pesa
Coinbase and other companies allow you to send bitcoins via SMS: https://www.coinbase.com/sms_service
Speaking from a technical perspective only, there is no way that Bitcoin can process transactions at a lower cost then a centralized method. A distributed log backed by proof of work is necessarily more expensive than a trusted, central server. Most claims of cost reduction come from the elimination of features, such as chargebacks, which will then be implemented by third party, resulting in unbalanced comparisons.
Supporters also point to smart contracts as cost-reducer, but the surface area where smart contracts can be made to work without human intervention is low, and I doubt many of these hypothetical cost reductions will be realized.