Are you talking about using something like this? http://mountainhomebrew.com/ProductImages/2177.jpg
If so, thats probably not a good idea. The headspace doesn't really matter in the primary, but I am not sure you can get a tight seal on those, like you do on the plastic pails made for use in brewing.
Also, you can't just drill a hole in the lid and shove an airlock in there. You need to be able to fit a bung for an airtight fit. Otherwise, you should look into the discussion regarding no airlocks on primaries - it's all the rage...
Also, the cooler is insulated, really well. Most people use them as mashtuns for that reason. Temperature control during primary fermentation will be an issue as a result i.e. you will be too high and not know it because those sticker thermometers won't work on an insulated device. So now you have to either geuss at your temperature or drill a second hole in the lid for a temp probe. Wow. What a headache. You should just buy some ale pails instead of trying to reinvent the wheel.
'Allow 6-8 weeks for delivery'
Thinking about: California Common, Fat Squirrel Clone
Fermenting: Greenbelt Pale Ale
Aging: Strong Scotch Ale, Robust Porter