It would depend on what you are doing. The information that has to be sent over the bus has very little to do with the actual resolution and much more to do with what information is necessary to form the image on the screen. The GPU handles processing instructions for manipulating and rendering shapes to be displayed. This is a big part of why GPUs are necessary. If you are planning on simply using desktop applications and Internet, I would expect that you would probably be ok. If you are planning on playing a modern game on all the screens with the resolution and texture qualities cranked, you "might" run in to some frame rate issues.
In general, as long as you meet the requirements for the card's interface, you should be ok for the most part.