Not sure I follow. Yes it would be more expensive (obviously) but why would that make it less portable? For me, its an ultra portable business machine on the road and a gaming machine when I'm docked at home... Perfect. Depending on pricing, I bet its cheaper than an additional $1500 for a gaming desktop.
I should clarify then.
When you mention external GPU, I assume you mean as a part of the dock - something that is for stationary computing, powered from the wall.
It will also depend on what you plan to play, as any decent graphics card will be bottlenecked by the CPU.
Games I play like PlanetSide 2 and Arma 3 require a high end CPU.
If you were to try running these games, or any decently specced game, on the Surface processors, the stresses of the high temperatures are likely to significantly shorten the lifespan of your device.
So you could do it. Play games like counter strike with good graphics, still struggle to run anything demanding a better CPU, but the stresses on your device would be immense.
I would go for the gaming desktop option with better ventilation, so that playing games isn't killing your computer.
I am biased though. This external GPU option isn't tailored for me, and I already own a good gaming PC. It could be an option for you, but you should give some thought to how long you expect your Surface to last.