Ordinary xenomorph drones are shown to have an understanding of cause-and-effect, as demonstrated in Alien: Resurrection when first they slaughter one of their kin to escape their confinement, then turn the liquid nitrogen that's been used to control them against their captors.
However I do not believe that understanding extends to lights and electrical wires, because the drones have not demonstrated this "ability" at any other time in the series, even at times when it would have been extremely useful/advantageous to do so. While they can see that pressing a switch performs an action, they have no way to know or intuit that said switch is connected to the light by a wire and that the wire is what makes it all work.
It is true that the drones have, at the time of Aliens, been alive for far longer than most xenomorphs in the series, and as such they could have observed humans performing maintenance-related work involving wiring and drawn the association from there.
In Resurrection it is possible drones could have been exposed to an experiment that e.g. put two simple circuits next to each other, then broke the wire of one to demonstrate that the light goes out - but of course that occurs after the events of Aliens.
In my opinion, the lights going out on the Marines is due to one of two things:
- Hadley's Hope was already pretty smashed up from the desperate battle between the colonists and xenomorphs. The power supply in that sector could have been quite literally connected by a thread that just happened to part at that moment, or was parted by the drones encroaching on the Marines' position.
- Interference (directly or indirectly) by the xenomorph queen. Queens have consistently been demonstrated to be far more intelligent than their drones (for example the queen from Aliens was able to control the elevator and stow away on the dropship), so it's no long stretch to consider that the queen either sabotaged the power at the most opportune time, or instructed one of her drones to do so.
The second feels like the most likely explanation, and the unofficial wiki seems to agree with this assessment.
So yes, the xenomorphs did intentionally cut the power, but it was most likely the queen and not the drones responsible for doing so.