I'm not so sure... I ran Esseles last night with my Consular duo and their companions (nobody else in group). Every loot drop except from the Sith was a Trooper/Smuggler item. The Sith dropped a light saber, but it seems to be 50% saber, 50% blaster from what I've seen (I've seen groups of 4 jedi get a blaster drop).

So at least at the lowest level flashpoint, it seems to not matter who is in the group.

The problem with these is that the majority of the ones I've seen are BOP, so it's just vendor fodder. I wish I could at least send them to an alt