Yes, you're absolutely right. The reverse is often also true. The funeral in Four Weddings and a Funeral, for example. A spoonful of salt helps the sugar go down.
Or the subject matter itself can be tragic - Islamic terrorism (Four Lions), nuclear apocalpyse (Dr Strangelove), for instance. Yet the above two films are absolutely hilarious, savagely dark comedy/satires.
Even something as silly as The Man With Two Brains has (absurd) tragic backstory thrown into the mix. Only at the silliest end of satirical comedy would this principle perhaps not apply. Monty Python and the Holy Grail would be an example, but even then, there is - I believe - a serious implied message inherent in the surreal hilarity, pertaining to the tendency of mankind towards violence.
Very interesting. You've given me a lot of food for thought.