I have never had an engine stop or sputer during spins in the dozen or so types I have spun. If the engine did sputter, I would really wonder why. A gravity feed fuel system might be afffected by a momentary reduction in G during the push over, but only once, while spinning an aft loaded C 206 did I momentarily get to zero G. I cannot imagine in an erect spin or recovery in a GA aircraft getting to zero G long enough to make an engine sputter.
I have sputtered engines momentarily during aerobatics, and certain very specific flight test maneuvers, but it's a non event. One of the required tests in the DA-42-L360 was a -0.5 G push over for a specified number of seconds. That did produce a sputter, but they came right back with positive G. Observers on the ground reported seeing clouds of white smoke during the zero G. Turns out that the engines each threw out about a liter of oil!