You do want to connect to the mixer, but you’ll need permission and help/cooperation from the audio operator.
(Plus the proper connections, of course, and a thorough TEST well before the program begins.)
AND, (on the other channel of the camera) you’ll want a mic in the room.
Audience APPLAUSE is always a part of a good recital recording.
You might want to put your live mic near the stage to pick up any sound of the dancers’
shoes, and other “natural sounds” that occur.
Be sure and WEAR good HEADPHONES throughout the entire event while you record.
That way, if you hear any PROBLEMS as you record… you can address them ASAP.