Can you apply for a work permit while on a Non-O marriage visa in Thailand?

Yes you can get a work permit on a non-o dependant visa / spouse visa

You simply need to be on a visa/extension that is not work restricted to be eligible for a work permit. A work visa is obviously not work restricted, but a marriage visa is not work restricted either.

You aren't the one who applies for the work permit, it's the company that applies for it. You are eligible for them to apply because your permission to stay allows it.

Many companies do not like their employees to be on a marriage extension because then the company cannot control them and threaten to get them kicked out of Thailand. Some companies won't even allow employees unless they cancel their marriage extension and switch to a work extension.