Well heck, you don't NEED a run at all, you can keep chickens alive and, if you're lucky, noncannibalistic in much less space and none of it outdoors.
It is hard to assess "happy" without things to compare it to, though.
(I can tell you that my chickens behave VERY differently at 15 sq ft per chicken indoors, plus run, than at 4-6 sq ft per chicken indoors plus run; and even with 15 sq ft per chicken indoors, they behave VERY differently when the run is available than when I've had to shut it for weeks or months for construction etc. If you saw them in the smaller space you'd think 'oh, they're fine' but then when you see them in the BIGGER space you realize just how much finER they can be...)
Two other things to bear in mind: many people do have problems (like, cannibalism) in small spaces -- the less space chickens have, the greater the likelihood of that arising -- and you are just not seeing them because those people either got out of chickens in disgust, or enlarged their quarters. And secondly, once a cannibalism/picking problem starts, you cannot always stop it just by enlarging the coop/run -- sometimes the habit is unbreakable and the only solution is a lot of chicken soup and starting over with new hens.
I guess my take on it is: you can try it if you really want and know the risks. Possibly you might get away with it. However your chickens would really be happiER (and your sanitation chores will be easier!!) if you give them as much space as you possibly can. There is nothing magic about any particular number, and honestly I think the 4sqft-10sqft numbers usually tossed around on BYC are pretty SMALL for chicken happiness.
So, personal decision.
Good luck, have fun,
Pat