From my experience a couple of years a go no, they come up full size on dropbox. I ended up having to use photobicket to upload photos at a board friendly size.
Maybe they have changed it, but with my new phone I get Google drive which I've found to be also as useless so still have to use photobucket.
Just testing with the dropbox app. Copy link, inserted it as an image and I don't see the image above, just a little box. I wonder if you could share the image from dropbox to the Photoshop app to get a correct link for boards?