Way too many variables. If you knew how warm the chicken was before cooking, how hot the cooking area is (and whether that will change during the cooking time), how thick the chicken is, whether you're cooking white or dark meat, and more, you might be able to make a good guess.
I would not recommend cooking just thawed, thick pieces of chicken on an uncovered grill. Too easy to make it hard on the outside and dry on the inside.
I wouldn't estimate lower than 20 minutes, but it will almost certainly be longer.
Edit: Here's a "Good Eats" video about doing chicken on a grill. http://www.youtube.com/watch?v=aAvy4YksJgM&feature=related It's better to go ahead and cut the chicken up the rest of the way for grilling so that each type and size of meat can be on it's own cooking schedule.
Roasting
I use direct heat, medium-high to high, specifically I use my grill but I've seen people set them directly on a gas stove burner (this seems like a fire hazard, so don't walk away). You could also broil them very close to the broiler, or roast them, but roasting will take longer than direct heat methods.
To easily peel them, you want to go until they're as black as possible. The blacker, the easier they are to peel. On my propane grill on medium-high flame, this takes about 4 minutes per side, my grill burns a little hot so you might need 5-6 minutes per side depending on how your grill works. edit: I also keep the lid closed so the flame climbs a bit more, especially important on a windy day.
You can find a picture on the top of this page, I actually let mine get significantly darker than that, but it's not required.
There are some great general roasting tips in this thread as well as peeling tips in this one.
Grilling
For grilling peppers, instead of keeping them whole, seed them and then cut them into quarters and lightly coat them with a little oil. I still use a higher, direct heat, but I flip the peppers more often so they will char a little without completely blackening. Since you're just going for a light char, this will take a little less time than roasted peppers would, about 8 minutes compared to 12.
There is a good step by step guide with pictures here.
Best Answer
If it's any good, it will be gone long before it goes bad in the refrigerator. :-).
I've saved my homemade barbecue sauce for at least two weeks in the fridge. Store-bought barbecue sauce lasts for months. You do need to put it in a sealed container.