I don't think it would be waste of time to try, how old is the starter and how did you make it? From my reading it seems most of the wild yeast/bacteria in a sourdough starter are on/in the flour already, in much the same way that when you do a sour mash you are using the lacto/etc. on the outside of the grains. The only problem I could see is that the starter growing process builds up those critters that consume dough, not wort/sugar. But I'm not sure that will be a problem. Try a one-gallon batch and if it turns out well dump it into a four-gallon batch. Good luck.