Quick and Easy Questions (please read the OP)

[Amaterasu]

In the interest of keeping questions such as this out in the open, in case anyone else has similar ones:

For faction quests where it's an either/or or a 'Pick one' scenario (specific example in this case: Coruscant and Hand of the Empire or There Are no Lines), I'm aware you can only do one and get the rewards for it. Question I have is, though, just for clarity's sake: can you still do the other quest, to unlock other things that it's required for?  Specific instance again in this case: I've already done Hand of the Empire, but there's another quest I wanna do later on that requires having done There Are no Lines. Discounting the OM/Influence rewarded from that, could I still do it to 'unlock' the other quest for later?

Adding to Blarghman's question: if it IS possible to do the other quests, would it be possible to earn the cosmetic rewards from the second quest that you do, while discarding the more "tangible" OM/Consumables rewards?