If you want to try attempting that at a maximum of 10 KBPS, sure.
For all practical purposes, the answer to that is no.
Discussion
Sad, even too light for handling a monero transaction
You might be able to create a protocol that would broadcast a signed Monero transaction, but it would probably take something like 10 messages to do it, since each message is like 200 bytes.
That might be, at least in the realm of possibility, but synchronizing a wallet is definitely not going to happen.