Alienware Laptop External Monitor / Resolution Question

So I have an Alienware 17 R2, and have decided to purchase an external monitor for my laptop.

I have decided to purchase a BenQ XL2411Z 144 hz monitor for CS:GO. I should probably upgrade to a desktop, but I don't want to drop that much for a whole new system yet, I'd rather get the peripherals before getting the tower and such.

Due to quality and pricing, I'm set on that monitor specifically, but here is where the question really comes in.

As it is a laptop, with an integrated Intel graphics card, but has a 970M Nvidia GeForce built in, I can set the native resolution to 4:3 but I cannot stretch it to the full size of the laptop display. With an external monitor, would I be able to have the Nvidia card "take over" and allow me to do a 4:3 stretched resolution for CS:GO on an external monitor? Or is this not at all possible, and I would have to purchase the Alienware Graphics Amplifier?

I want to see my options before I actually go spending any money. Either way, I will probably get the monitor, and if I cannot do 4:3 stretched, I will just play 16:9 with 144 hz.

All help is appreciated! Thanks in advance! :D