It would be easier to just add Dropbox to the LEFT side of your start menu by using the pin to start menu option. The right side is a bit different. You can right click an item on the start menu, choose properties, and then click customize and see if you can do anything from there. Not all the items on the right of the start menu give you that option, but some do.
Also, right click the taskbar, choose properties, start menu tab, customize: That's the only ways I know of to mess with the start menu........ Hope it helps:)
Maybe someone with more knowledge has a better idea?