NO.
Do Not use MAPP to anneal. MAPP gas contains relatively little propane, not that it matters, but the flame contains high levels of hydrogen, which does. In conversations with D. Dorris (maker of Bench-Source machine) he explained that exposure to MAPP can have the effect of making the brass structure brittle. Exactly what we're annealing to avoid. Stick with propane.
I have rigged mine to run both torchheads from one ten-gallon tank. PM me for the how-to.
Bob