Will this monitor work?

It will work great. Either get a Mini DisplayPort cable to (regular) DisplayPort cable, or an HDMI cable. I prefer miniDP just because it plugs into the same side as the other most useful ports.

 

It can drive at least 3 of those monitors at once in addition to the built-in screen without breaking a sweat.

Use DisplayPort as suggested above. The fact that it also has VGA/D-Sub suggests it's an older monitor, so its HDMI port may not support the full resolution.

 

Use the mini-DP -> DP cable for less likely to have issues.
I wasn't able to get a newish BenQ display running with mini-DP/TB -> HDMI at 2560x1440, zero issues with mini-DP/TB -> DP.

True, it may have been the cable, but tried a few on hand.

 

If it is an older monitor you might want to consider whether to use it or get something newer. I have a couple of Eizos I love, but then I look at the specs, connectivity, and PRICE of the newer monitors, they Ezios are destine for retirement.