Yes, the Google Translate app has a conversation mode which doesn't require a headset at all. I wouldn't recommend trying to use it with an unsupported headset, though. You won't be able to do push-to-talk, and the audio routing won't work as intended. (The intended UX is that one side of the conversation is routed to the phone, the other to Pixel Buds.)
I wrote about why we decided not to support third party headsets here: https://news.ycombinator.com/item?id=15404918