HomePod mini and FaceTime

Yes. See Use HomePod for phone calls - Apple Support.

tt2

Interesting. The article doesn't make any obvious distinction between HomePod and HomePod mini here:

Use HomePod for phone calls

HomePod uses your iOS or iPadOS device to place and receive telephone and FaceTime audio calls (iPhone is required for telephone calls). To use these features, you need to set up your iOS or iPadOS device to make Personal Requests on HomePod.

I will admit to not testing it personally before I posted, but it works for FaceTime audio calls. Given that AirPlay can introduce lag I'm not surprised if you cannot use HomePod for the audio component of a video call. That would likely get confusing.

tt2