It depends on whether you define the end of the combat to happen before or after the "winning invasion" step. For instance, shock troops are formed at the end of a round of combat. If they started and left on the last combat round, they don't capture the PDSs/SDs, but if they are formed during the last combat round, and at least one other GF remains, they do capture the PDSs/SDs/facility.
It's obvious from this that "end of [the last] combat round" happens before the "Invasion Success?"=true. So it's up to your group to decide whether "end of combat" happens a) simultaneously with the end of the last combat round, b) between the last combat round and successfully invading, or c) after successfully invading.
The same goes for copying Salvage Operations at the end of Space Battle with Mentak.
For what it's worth, the numbered breakdowns of Invasion Combat and Space Battle Sequences don't include victory/loss, though those are included under the sections of rules involving Invasion Combat and Space Battles.
At any rate, the Nekro can copy Nano Tech from the space battle or a different [poorer] planet in the same system during the same activation and use Nano Tech to refresh the remaining planets in the system, upon successful invasion. It's only that first planet where it can matter.