Hmm, I'm not sure where that error would come from. My first guess would be that Dropbox sees these files, tries to open them in order to sync, and this other app tries to do something with the file that's denied because Dropbox has a handle open to the file. When syncing files, we try to apply as liberal a set of constraints as possible, but unfortunately on Windows it's not possible to fully prevent interference.
In the past we've handled this by checking filenames against a set of patterns used by specific apps, and then backing off on syncing those files for a while, in order to give the app time to do whatever it's doing.
We could potentially add a similar rule here, if we can identify a specific pattern in the filenames this app uses.
To answer your question tho, Dropbox doesn't currently expose any API surface that could be used to programatically [un]pause sync.
