Dropbox's device limit does not apply to apps like Road Trip. You do not need to install the Dropbox app on your iPhone or iPad in order to use Dropbox Sync in Road Trip.

Road Trip will allow you to securely sign in to your Dropbox account when the Dropbox app is not available. If the Dropbox app on your iPhone is no longer linked to your Dropbox account then you should remove the Dropbox app from your iPhone.