NO!
Connect them both, and use a dual monitor setup. By far the best end user improvement to any 3D hobby desk is a dual monitor setup.
Even this little 10" netbook that I am using right now, has a second monitor. The netbook screen at 1200x800 or something, and an external 21" 1920x1080 monitor.
Once you go "dual", ha-ha-, you"ll never go single again. LOL.
Euh, I mean monitors, OK?

PS : the photo is from an older setup. There are 2 extra screens right now. LOL.
Left, 21", then a 25"; then a 50", and the one to the right is a 32".

Poser 1, 2, 3, 4, 5, 7, P8 and PPro2010, P9 and PP2012, P10 and PP2014 Game Dev
"Do not drive faster then your angel can fly"!