It could be a solution in the future, but I think that most rural places in Africa still do not have access to good internet. This poses a problem for widespread Bitcoin adoption there.
A friend of mine recently gave a lightning talk at the Git-Merge conference, which explained this problem and offered a solution, using Github as a money-less transaction exchange ledge system.
I know this doesn't have anything to do with Bitcoin really, but I thought it was pretty interesting, I'll copy the gist of the talk here:
“Lightning Talk / Git: The Original Blockchain”
Meredith L. Patterson, Mautinoa Technologies
Meredith showed how Git was chosen as the underlying platform for implementing a money-less transaction exchange ledge system. This implemented an actual monetary system in Sierra Leone, where phone minutes is actually considered a viable FX currency, since otherwise the national bank would go bankrupt.
Bitcoin and other blockchain-based distributed ledger systems are “gossip protocols”, and require always-on Internet access, not available in much of Africa. What is needed is a way to perform transactions off-line, with later reconciliation step. This means that the system needs to store timestamps in its blockchain… Meredith noticed that this is what Git does! The presented solution uses a ledger-cli / hledger plain text accounting format as a format for storing transactions, Git commits for blockchain, remotes as wallets / accounts, and GPG keys with short expiration dates for signing.
This shows how technologies, such as Git, that do one thing well can change the world by doing the thing they do well in unexpected places.
Source:
https://git.github.io/rev_news/2017/02/22/edition-24/Sadly the video isn't up on their website yet.
Electrum can keep only the transaction related to an address on the local computer, not sure it can get directly the balance or compact summaries from the node, but anyway if you want to check an address, you still want to have a minimum of the history for the all transactions. After it's more in having more advanced filtering to minimize the data that has to be transmitted for the operation, if it's just to send a new tx to the network, you can already do this via web service who have up to date node.
There are some system already of off line signing, but the risk is double spending, if the output of the off line signed tx are spent before the reconciliation, it will be an invalid transaction.
It's a bit also the downside of decentralized network, they need to rely on gossip and can lead to more bandwidth and ressource use to sort and validate and synchronize everything from everyone, the solution with git - like thing seems to go back to a form of centralization to minimize individual processing and synchronization in case of scarce resources, but it become somehow another system, more based on centralized trusted server to process validate and optimize things for everyone.