Never tried it, but if its food grade plastic, I don't see any difference between this and a better bottle/fermentation bucket. Obviously you won't be able to see the clearing, but it should be just fine in my opinion.
Not sure how you would add an airlock (as mentioned), but not sure you would need to either. I think if you just turn the lid one screw (as opposed to 3 when its tight) it should keep out most air/bacteria, but also allow pressure to escape.
Give it a shot and let us know?
PS - Why would you use a 3 g cooler to do this? Why not purchase another $6 bucket or $20 carboy? Is it just what is handy or what? A 3 g cooler costs $18, so not much cheaper than a carboy.