Can I reveal the base's location to bring the fleet from the Rebel Base into the battle above the system?
Seeing as that fleet is in the system anyway.
Empire (No ground units) attacks visible Rebel fleet in system where Rebel Base is hidden, with it's own fleet. Can the Rebel Base fleet participate in the battle, revealing the base.
No.
As long as Rebel base is hidden, "Rebel Base" space and the system containing Rebel base are two different, separate "locations".
For refference, this is when the Rebel player may choose to reveal the base:
"If the Rebel player wishes to optionally reveal his base, he can only do so at the start of one of his turns of the Command Phase, either before using one of his leaders or passing."