Dropbox is always connected and continually checks for updates, just because one sees at the same time doesn't mean they are related. I see Dropbox connections all the time whenever I look through my network.

I am on mac, I have littlesnitch and I also have Geektool display network connections. Dropbox is not always "active". I don't see any kind of network traffic after syncing has been done under macosx.

It needs to at least be periodically active to sync in case you add a file with another device.

Periodically yes, but open TCP connections can technically last for days (although this is implementation-specific) without any packets being sent across.

You're right of course, periodic data needs to be sent even if just to keep the TCP connection open, but it's not much and it's not often.

This can be simply analytics event tracking.

Correlation does not imply causation.