I suspect "warm" is meant to maintain temperature, rather than raise it. My crock pots are too ancient to have anything other than "high" and "low", so I can't assert any real authority. However, if you reach 145F within the first hour at the highest setting, then keep it at "warm", and test the temperature after about 30 minutes with an instant-read thermometer and it stays around 140-160F, you'll probably be fine. Personally, I'd test the temperature first by cooking water.
If the temperature stays above 140F at low, the worst risk you'll have is overcooking. Beans and vegetables like carrots and celery can overcook fairly easily in a crock pot, but higher collagen meats meant for stews tend to be fine when cooked for extended periods. Most crock pot recipes for stews and soups usually hold fine when at low for a full workday, although that's presuming a somewhat 70s-era soup aesthetic, which is probable for a crockpot recipe.
However, I would be inclined to attempt the recipe using the low setting rather than reducing it to warm, if you're not going to test the temperature first. If it turns out to be overcooked, you can always puree the ingredients with a blender...
I also doubt that switching to "warm" would be dramatically less likely to overcook the food than "low", unless it holds at a pretty stable 140F, and low ends up somewhere around 160F.
If you keep the lid on, it shouldn't make much difference in practice.
The thing to watch is that the larger surface area and heat supply of the 6 qt pot might make the recipe cook a little quicker than it would in a 4 qt pot, and also make it dry out quicker than it should (which is why you need the lid on). Just take a look after about two thirds of the time and decide if you should add a little water, or not.
Best Answer
You could cook it for less time, but it equally wouldn't make much difference if you just went for the full 6-7 hours, especially if you are using a forgiving cut like thigh.
I would, incidentally, be very wary about putting frozen chicken in a slow cooker. At the low temperatures a slow cooker uses, there is a good chance the chicken will be sitting in the 'danger zone' for longer than 2 hours, increasing the chances of food poisoning drastically.