More than any place I have ever seen, Disney will bend over backwards for food allergies. There are plenty of potentially dangerous dishes, but at every table service restaurant -- a chef will gladly meet with the family and discuss the safe dishes. The chef will typically even prepare something special if necessary. That's regular restaurants...
I can't speak for certain about the club level, but I doubt there would be quite as much customization, as they basically just lay out buffets. I'm sure they could get information about the allergens in the foods.
The "value" of the club level is quite subjective. Some would say, it's not worth is for anybody -- Even if you eat all the food provided, you probably are not getting your money's worth in terms of food, compared to the price of a regular food.
You can research what types of dishes are generally available at the club level at the Yacht Club. Depending on the children's allergies, much of the food may be very friendly, or very unfriendly.
One can say that the allergies diminish the value of the club level -- if much of the food would be off limits for them.
On the other hand, one can say that the club level adds extra value with severe allergies -- As the club level includes concierge and trip planning, which could help the family contact the chefs and arrange for allergen-free meals.
My own son has some severe food allergies, but at this point, it's basically nuts, peanuts, and some egg products. It's been pretty easy to avoid those items at Disney and elsewhere.
For people with glutton or dairy allergies, for example, it can be much more challenging.