Yes... but I think my opinion may come off a bit harsh.
Based on many studies, by many different groups and individuals over the years, and based on my own experiences... it is my OPINION that a 7" Barrel is very limiting, and borderline worthless. I personally would build that on a pistol receiver, if i was to build one at all.
In truth, I don't really see a need for a stock on something like that, unless it was an HK type side folder. Use the buffer tube as stock or just setup a sweet little K-Gun style tension sling and slap a dot sight on it or w/e. Make a nice little PDW, and use the tool for the job it's intended for. The hammer your thinking about making will not drive screws as some other hammers will, not efficiently anyway... Besides, with a pistol receiver there is no SBR papers and ATF love... no tax stamp... etc. etc.
If you want a legit CQB assault rifle, not a PDW, I would do a Noveske 12.5". It's short enough to be easily accessed in a vehicle or in a small hallway, whatever the case may be. With the 12.5" you retain a good degree of range/accuracy and ballistics within reason. 10.5" is still a bit short for ranged targets, but a 14.5" is too long for most tight CQB work.
Remember, that a 7" barrel is roughly 1/3 the length of the original design. Subsequently a much much shorter gas tube, which alters the locking time of internal parts. This can cause stress on locking lugs, bolt, cam, etc etc.... The reduced barrel length does not allow for maximum pressure build up which causes several things to happen regarding ballistics, and often times leaves some powder not fully consumed. This unconsumed powder creates sparks and falling cinders form the muzzle. Sometimes these sparks like to set bushes and trees and Caswells Shooting range on fire... no joke. Usually need a good 2 or 3 baffle comp to reduce the amazing flame and sparkage...
There are lots of variables to compensate for if you intend to do it right. Will a 7" work if you just slap parts together??? Sure, Probably, who knows, why not... but why do it like that? Gotta do it right if your gonna do it at all. Research the ins and outs of shorty barrels. lots of people have done the work for you already, just gotta read about it and make your own decision.
ACE-OF-SPADES