I have not heard of anyone successfully using Dropbox to host a back end JET (.mdb) or ACE (.accdb) database.
I found it must better to use an SQl Server back edn when hosting it out the internet (now called the cloud).
I alos rreally like using a Thin Client technology. I use Terminal Services a lot.
You may also want to see some of the other optons listed here:
Running an Access database over the internet