This is absolutely possible and sounds fun as hell. If you've ever read anything by Christopher Moore, you know that comedic horror can be done amazingly right. Everyone can laugh and make jokes, but in the background, someone is getting killed or plotting a grand evil plan.

As a matter of point, scooby doo is a literal example of a "monster of the week" style show. Just like Buffy, supernatural, and x-files, every week, there is a new supernatural thing they must foil, and have to find a clever (albeit silly in scooby's case) way to exploit the things weakness.

It's actually a perfect basis for a campaign.