Does Discord have a native voice recorder?

No. Discord can't record a whole voice channel by itself.

What Discord has is Clips. Clips saves the last 30 seconds, 60 seconds, or 2 minutes of a stream when you press a hotkey. It's good for grabbing a funny moment. It won't record a meeting, a game night, or a podcast from start to finish.

Recording the full session

For that you need a bot. With pawa:

1. Invite pawa to your server.
2. Join the voice channel and type /record.
3. Type /save when you're done.

You get one MP3 of the whole session, up to about four and a half hours. The full walkthrough is in How to Record a Discord Voice Channel.

If you need each person on their own track, Craig does that. See Craig vs pawa.