Yes... and no. It depends on how you define that. You can play Amazon Music via AirPlay (open app > select music > press Play > cast to Homepod mini via AirPlay). It gets the job done, but as someone who just bought a Homepod mini after having used an Echo Dot for years (whose privacy issues and opt-out only global device network are dealbreakers for me), it feels like a big step backwards.
You *can not* play Amazon Music hands free. Meaning, you can't say, "Hey Siri, play [album] by [band]" and get results from Amazon Music.