Yes! Since the Chazorai Arena (mortal combat area) is not considered as a "lever boss room" you can bring your familiar with you.
You can use the spell to Summon the Familiar before going to the room and enter the area with the familiar. Or you can even use the spell inside the room during any time of the fight, so that you can save your familiar to when it's more convenient to use it.
Keep in mind that Familiars only last for 15 minutes after being summoned and there's no time limit for the combat at Chazorai arena.