Suppose I have a trooper squad with only two guys remaining. The leader is hiding behind full obstruction cover and has no LOS to the enemy, but the second trooper has LOS to an enemy in the open. Can I shoot the enemy even though the leader can’t see anyone?

Yes - if you read the Attack section of the RRG, it does not require your unit leader to have line of sight. You only use the unit leader to determine range and cover. So if your second trooper can see the target, he can attack. If the unit leader (or any other minis) can't see the target, they don't contribute dice to the attack pool.

Additionally, the target would receive the agreed-upon cover for the blocking terrain, unless your unit leader is in base contact with it.

2 minutes ago, Turan said:

Additionally  , the target would receive the agreed-upon cover for the blocking terrain, unless your unit leader is in base contact with it.  

Easy-to-miss detail, but when LOS is fully blocked you actually get heavy cover regardless of what was agreed upon (unless in base contact as you said). From page 8:

Quote

Terrain either provides no cover, light cover, or heavy cover,
depending on its characteristics. Terrain that completely blocks
line of sight always provides heavy cover.

I did miss that, thanks!