No - faction status also is irrelevant for Powerplay. The major powers are above those petty squabbles (or that's what they want to make you believe, in any case...).
So, Eravate:
The companion site for Elite:Dangerous with the game database, market data, trade routes, outfitting, engineers, blueprints, crafting, Thargoid war, squadrons, logbooks, galleries, galaxy information and much more...
inara.cz
Currently a Federation system (and, since it's under the wings of Adle's Armada, likely to stay that way), and exploited by Zac Hudson. Could be worse. If you want to engage in Powerplay, you can pledge to Zac Hudson. If you want to engage in the BGS, you can check if Adle's Armada (one of the larger player groups) is recruiting. Either are independent from each other - Powerplay (PP) is an ingame mechanism - similar to "Risk" or other world domination games. BGS is the Background Simulation in ED that controls the states and allegiances of most of the systems (a few of them, like the Pilot Fderation district and ShinDez, are locked), and player groups as well as individual players act to move it their way. Those player groups usually coordinate and talk outside the game.
If you want to pledge to Zac Hudson, go into the "Powerplay" tab (from your right HUD, IIRC) in the game. Then read what's written there about Federation - Zac Hudson and pledge, if you want to. This will make you/your ship marked as Zac Hudson supporter, and anyone (NPC or player) from an enemy power is now free to shoot at you in the name of their patron - and vice versa. It will also get you a moderate (unless you actively engage in PP by killing enemy ships or supporting Hudson's expansion) weekly income and, after 4 weeks' time, access to the Pacifier - a rather nice class 3 fixed shotgun.