I think this depends on what your usual eff. is, I mean, if you get 65% usually, then sure, as there are plenty of sugars still in there for another sparge for your braggot. On the other hand though, if you normally get north of 80% or so, then there's almost nothing left to sparge out, and your mead would just have a very very slight maltyness, with some tannins from oversparging. When doing this most that I have seen do it partygyle style, using the first runnings for the "bigger beer" in this case your oatmeal stout, and the second runnings for a braggot, I believe BigKahuna did this for his holiday stout, maybe he'll pipe in soon.