Neonchameleon
Legend
If it is fun, then it'd because your group would have just as much fun doing improv theather as playing D&D, because the rules are actively discouraging fun in an unbalanced game. Or because everyone accepts it's unbalanced and the rules acknowledge it ala Ars Magica or Buffy/Angel.
As someone who does both improv theater and D&D, no. D&D has many things Improv Theatre doesn't - the big ones being conflict resolution and the ability to have a vision.
Improv only really works under the principle 'Always say yes' - when someone says something about the person you are being you accept it. If you start saying 'no, I don't think I'd do that' the entire scene grinds to a halt.
This means that the space you can explore using Improv is limited in a way D&D isn't. You're going to spiral out of control fast; with no DM and no conflict resolution the world's going to be gone. There's no possibility of D&D style 'step on up' play or even bright ideas not working other than in the Fiasco sense (Fiasco to me blurs the lines between improv and tabletop). And you shouldn't be trying to plan anyway in Improv.
Not to say there's no 'Step on up' at all in Improv - I know groups who can improvise a 30 minute musical off a location, an event, and 5 song titles. But you do that by accepting every idea someone else on the stage throws at you and expanding on it rather than whittling it down to work out what will work with some sort of limitations. And I don't believe that an ongoing improv would be at all possible in the way you can have multi-year D&D campaigns.
So although there are a lot of similarities, the fun you have with the two is very different.