Azerite Traits while leveling I think don’t really account for much dps. Also the heirloom pieces still have the usual secondary stats so it should be a little under the value a Azerite piece would give while leveling. Considering your time to kill mobs won’t be too affected the trade would be worth it for the bonus xp.
TL;DR: Yeah they won’t have Azerite but the bonus xp is the point of them. I can’t imagine you’d notice too much of a difference but if you’re testing it on the PTR please let us know how it feels.