Sure, you can. However, you cannot pack perishables inside it, and the agent who checks the bag is responsible for visually inspecting the inside to see that it contains no perishables and no water ice. (There are special rules for checking perishables, which allow ice substitutes, and the specifications for the container are quite strict. Consult the airline if you wish to check perishables.)
You need to rig a way to keep the lid closed that will allow for the possibility that TSA will open it; we use two luggage straps.
The usual weight/size limitations apply. Nothing over 62 linear inches (L + H + W) unless you want to pay a hefty oversize fee. Weight limits vary, but the max without the fee is usually 50#; again, check with the airline to be sure.