Can my Japanese friend obtain a work permit with a Non-O (dependent visa) in Thailand?

A Non-Immigrant Type O <- the O means "other" visa is issued for a variety of reasons here; married to a thai national, raising half thai or foreign children here, being married to a foreigner who legally works here, volunteering, etc.

The only one that can't hold a work permit is the one based on being married to another foreigner who works here and that's because your Non-O and extension are tied to your spouse. All the rest of the reasons CAN legally hold a work permit.

You can get a work permit with a Non Imm O based on dependency