I'd find that awkward, personally I'd just plug in a mouse and be done with it.
It all comes down to power but the 13" is more capable than most folks think, unless you're doing a lot of high res photo or graphic work the 13" is more than capable for most Photoshop and related tasks.
I guess that would work. If I was using the monitor I would use it for large engineering projects in a single program which means my need for a keyboard at that time would be limited. (Wouldn't have keyboard shortcuts though) I guess I could use a tablet as a wireless keyboard?