That would be a really efficient way of downloading the block chain, especially for poor communities. You can use Bitcoin with even the most primitive dial-up connection if you can get the block chain.

It's probably possible to allow people to download a "block digest" containing the first few few bytes of all addresses in that block. This wouldn't work with non-standard transactions, but it should allow general use without downloading entire blocks. Even this might be too much data for super poor communities in Africa, though.