Well, sure. You can do that if you'd like. You could also get a very slim and flat HDMI cable, and bend it back from the rear IO into the monitor. =)
As for GTX 750 Ti, just because you have a dedicated GPU doesn't mean you have to push it to the extreme. Your GPU can run on idle if you need it to, and you don't have to push it past 60fps or even 30fps in your games. Limiting the framerate of your desktop GPU in a battery-limited situation is ideal in this case. Flexibility if you need it.
Moreover, you could also have it plugged in, but run your monitor off of the embedded display, simply by changing the default monitor and the default driver. =) You can have it all. You just have to moderate and not use it all at once.
As for having a power cable to go full-blast, you could get an i5 4670K, and rather than overclock it, you could underclock it. Lower it's clock for lower temps when you're not gaming and you want power savings, turn it up if you want power and you're connected to an outlet.
There's so much potential here. I'm interested in seeing what you build, how you mod it, and so forth. Make sure you take pictures and/or videos as you unbox it, build it, make it into a blog series, etc. It'd be nice. And maybe some glam pics at the end, just for bragging rights.
Maybe you could even start a blog series here on TekSyndicate, about modding everyday items or vintage technology into computers. Maybe that end table that's shaped like a wooden cube can be fitted with a matte, IPS monitor on stop, and a layer of glass added, while the bottom can house the IO shield, PSU, and more. You could use it as a dynamic board, in a board game. Or a dungeon that changes as you play, in your next D&D roleplaying session.
Add a couple of speakers, and plug it in, and you've got a conversation piece, an entertainment center, and you can add a few spacers (rubber circles) and a glass top, and you can still use it as a table and still see the display. Wireless keyboard with trackpad (like what Logitech just released), and you've got a great entertainment center with which to gather friends around, or maybe watch something while eating and drinking a beer. Maybe use it to show the score in your latest sports game, with the TV showing the game itself?
Basically, the idea of getting everyday items and putting technology in them to make them more useful, interesting and fun sounds like a great idea for a blog series. Heck, how about modding a desktop computer so it can power some tablet or smartphone displays (7" or smaller), to make a Star Trek captain's chair, or something like that? Or maybe set up several tablets together, and make a desktop arcade that resembles a Star Trek tactical console (TNG?), maybe playing a game that works well with touchscreen (FTL? or would that be an Inception of obscure and really nerdy tech references?).