I brew my own beer and have cultured yeast from many different beers. Beer yeast has developed over the years to maximize the production of alcohol........then CO2(which is the opposite of bread yeast). In other words it will work, but it's not the best choice for pizza or bread
It depends on the beer. Top fermenting ale yeast and bread yeast are one in the same (Saccharomyces cerevisiae). Lager yeast is a different animal.
Most commercial beer you buy these days is pasteurized. Pasteurization kills yeast. If you could get your hands on a homebrewed unpasteurized beer, then perhaps it might work, although, it should probably be an ale, rather than a lager. I don't think lager yeast is ideal for bread because of the lower temps required. If you can get homebrewed ale, ideally, you'd want to collect the yeast from the top and not the sediment. If the yeast is at the bottom of an unpasteurized bottle of ale, it's not going to be alive anymore.
I guess you could collect the yeast and proof it to make sure it's viable, but it seems like a lot of trouble compared to grabbing the bottle of confirmed viable yeast from the fridge.
I also don't think the alcohol is good for the fermenting dough. If you combine beer and IDY, the alcohol in the beer will fight the growth of the IDY. Gliadin, one of the two proteins in flour, is slightly alcohol soluble. There's nothing you can do regarding the alcohol produced by fermentation, but I don't think it's a good idea to intentionally add alcohol at the start of the process. If you like the flavors in beer (hops, roasted barley, etc.), it's probably a better idea to obtain the core ingredients from a brewer supplier and use that in bread- minus the alcohol.