I play FFXIV on a 28" monitor in windowed mode at 1920x1200 and have a second 17' monitor at 1280x1024 for notes, firefix, ect...
It can be done, but it will make you video card work harder.

And yes, there are ways to remove the window borders that do not violate the TOS.

Happy adventuring.

EDIT:
agreed you can't move the chatbox to a different screen.