The capacity region of a two-transmitter Gaussian multiple access channel (MAC) under average input power constraints is studied, when the receiver employs a zero-threshold one-bit analog-to-digital converter (ADC). It is proved that the input distributions that achieve the boundary points of the capacity region are discrete. Based on the position of a boundary point, upper bounds on the number of the mass points of the corresponding distributions are derived. Finally, a conjecture on the sufficiency of K mass points in a point-to-point real AWGN with a K-bin ADC front end (symmetric or asymmetric) is settled.