That’s the basic idea. You can install an application you buy from the App Store on any computer that is currently authenticated by your iTunes account. Do note that this is not universally true, though. Some applications you buy are single-seat only, such as Apple’s Aperture. This is something the developer can set, so always read the fine print.
There shouldn’t be any problem with that, unless I misunderstand what you mean by three-way. You can have dozens of computers using the same Dropbox folder if you want.