Can I use a larger crockpot than the recipe calls for?
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.