I'm assuming you are asking about nouns of mass versus units. Turns out the answer is quite interesting for both people and barbeque chicken. Essentially what you are asking is, is it "how much" or "how many" correct? Let's try using both phrases with each noun:
"How much barbecue chicken?"
This is probably what you would use or encounter the overwhelming majority of the time. Barbecue chicken as a food item is generally a marinated mass or pile of various chicken parts or possibly wings or thighs only. If you were talking about barbecue chicken WINGS, you would say "how many did you eat?". The reason "barbecue chicken" uses "how much" is because it could be any variety of barbecued parts from a single or several different chickens. "chicken" is unspecific, except for one case...
"How many barbecued chickens?"
If you ask this you are talking about whole barbecued chickens. It's best to add "d" to barbecue, though probably not strictly necessary. You can definitely say, "One (whole) barbecue chicken, comin' right up!" Of course if u do use "how many" u must make the noun plural.
"People" is a tough one. Let's try using everything just to see what works and what doesn't, and what it means:
[1]"How much people?"
---this is grammatically wrong. It sounds like swamp monster caveman-speak asking about an amount of human flesh.
[2]"How many people?"
---this is equivalent with the somewhat more "educated/pretentious" sounding "how many persons?"
[3]"That's a lot of people."
---here again, it seems like "people" is being treated like a mass word just like example [1]. After all, you would say "that's a lot of beef/pork/chicken/rice." But strangely, this in fact is equivalent to saying, "There are many persons." I think it makes sense if you think of "lot" as a measure word like "group, crowd, throng".