Yes you can compare these models if they are reduced forms of each other. The typical method is doing a -2loglikelihood test. No, your null hypothesis does not have to be "0". Though, you would have too have good information to propose otherwise.

Alternative hypothesis can also include: equivalency, superiority, and non-inferiority tests.

I will see if I can find any code for the likelihood test.

P.S., Does your M1 represent an intercept only model?

@Dason, what if M2 was an intercept only model and M2 was the same thing but a2 was a random multinomial variable not associated with the outcome. Thus, the intercept would be the base case, though the reference group has no explanatory power. Could that make the M2 model worse, base on some criteria?