Will a cold steep extract the necessary elements from adjunct grains?

If it's the head retention qualities of the flaked barley you are after, you could add 200g/0.45lb of carapils per 19l/5 gal. It will add head retention, and hardly adds any color, and such a small amount will not affect mouthfeel.

I usually brew my stouts with an Irish liquid yeast, but I've also used US-05 and then they come out really dry! If you use US-05, it's probably a good idea to double the carapils, to round out the beer a little. If you're used to drinking Stout on Nitrogen, but are bottling or serving on CO2, you'll loose the thicker mouthfeel that serving on N2 gives. You can add 300-400g/0.6-0.9# carapils can also help create a slicker mouthfeel.

Unmalted cereals always need mashing, since they contain no diastatic power, and can't convert the starches into simple sugars. If you steep, you'll extract some beta-glucans that give some of the mouthfeel, but you'll extract far more starch. In a light beer, it will be clearly visible. In a stout, well, it's not going to be all that visible - so you might try it. Oats are particularly good, and add a lot of smoothness even in small quantities (<5%). For the best beer, you should really mash, but if saving time is more important than getting the absolute best beer you can, then add a few percent of oats and the carapils and you should get a nice mouthfeel with a good head, and at the most a touch of cloudiness.

Nope. Flaked barley needs to be mashed. You'll get nothing but starch from it in your beer. Not only do you need a higher temp, you need some base malt in there an you need to do a partial/mini mash at least.