Non-retina MacBook Pro with monitor

Your MBP will display it in the native monitor resolution, so yes, 1440P.

 

Provided you use an appropriate adapter. The MacBook can easily support that resolution, but a cheapo adapter won't. I recommend using a quality display adapter, potentially from Apple. Although they are expensive for what they do, I have never had an Apple adapter go out. Also, use DVI or HDMI if possible to ensure the best quality.

 

As others said it will work... However ideal config is DisplayPort, which requires no adapter (just a mDP cable which plugs into the Thunderbolt port). DVI will work with a dual-link DVI adapter (must be dual-link, $99 from Apple, not a cheapie adapter - so if you have a choice of a display with DisplayPort vs one with DVI, take the DisplayPort unless the DVI is over $100 cheaper.)

HDMI won't work; HDMI adapters can't do 2560x1440.

 

My mistake, it just hit me that HDMI is limited to 1080. Eureakan is definitely right in everything he said. It may not be cost effective, but have you checked out the Thunderbolt Display? Not only does it function as a display, but also as a dock for your MBP when working. It replicates all the ports and has a built in MagSafe cord. Pretty great display quality too.