I've been running LPX on a 2011-era MacBook Air (13-inch) with no trouble thus far.
I find I close the library column often, because it takes up more real estate than I'd like, but I've use Logic 9 on 13-inch (and 12-inch) screens for years.
You can adapt the window to show you what you need to see at any given time, so I think Logic is great on 13-inch screens.
Bear in mind, that Screensets work just as well in Logic Pro X as they did in versions 4 through 9 in pretty much exactly the same way. So you can type the 2 key and open a Mixer from the window menu, type a 3 and open a Score window, et cetera, and easily toggle between those windows with the number keys.