Have you considered using a Terminal Server? That's essentially what hosted services are. They run a terminal server and you remote in. You can install one at your current office.
I don't how realistic real time synchronization of SQL is for a small office. I believe it's called transactional replication and requires a pretty steady connection. Not business class cable, but more like T1 line.
I think you're mixing up 2 things here. A hosted AC solution and the DropBox sync are two radically different solutions. You can't just sync the database with DropBox because it's being used. It probably won't sync until you shutdown the SQL server. A hosted AC solution would mean some third party provider would be hosting your database. There are hosted SQL services, but say good bye to AC support.
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