I just recently got a lawn tractor and was going to buy a core aerator
attachment, since it's been years that the lawn was aerated. But is it
also necessary to dethatch first?

Recently on Ask This Old House Roger Cooke rennoavted a lawn by first
dethatching, then core aerating, then sweeeping compost over the site
and reseeding. I thought that aeration was intended to take care of
thatch to a degree.