Yes, there are some very straightforward single failures on the 737 that prevent either autopilot from working, losing a single IRS would be such. It could also be a simple electric or a mechanical failure, such as a sticky AP disconnect switch or a closed circuit for that switch - can't engage AP if one the disconnect switches is pressed (or sensed as pressed).
737 up to including NG can be dispatched with both AP inop (outside of RVSM etc.), but on the MAX, at least one must be operative to provide MCAS functionality.