I brew also, but never got into wild strains and sour beers.
However don't think many of the "beer" yeasts would have the leveling power needs for the dough to rise and get its pizza like qualities without some major prep.
You would almost have to treat it like a starter that you would use for brewing and substitute the starter solution for the water in the dough recipe. It might be a LOT of experimentation to hit the proper part of the fermentation curve, but I would say its possible. There is a good thread about substituting beer for water and doing something like this would be very similar, but instead of using already fermented out beer, you would be starting with young sweet beer.
There are also other considerations such as heat tolerances of the yeast, PH that it needs to grow and etc.