I am guessing any node that can't keep up will automatically become blacklisted and they fall forever behind. Such low bandwidth nodes will need to run slim clients. Not sure how they will be able to send NXT
Slim clients will have to form and sign their transaction locally then transmit the transaction to a hub node. They'll have to poll the hub node periodically for some X blocks to make sure the transaction wasn't orphaned. If it gets orphaned, they'll have to re-transmit.
That's my understanding anyway.