Not really.
There is a controlling minor faction, but it's not an influence-holding one. (Pilots' Federation Local Branch)
(This wasn't how it was at the start, of course, PFLB used to be influence-holding like the Sol factions: the change seems to have mainly been part of C&P reforms in 2.4 and 3.0)
This faction also controls a few other systems - Asellus Primus, AY Indi and LHS 3447 - and some assets in other systems as well, and while those systems are not fully locked there is no BGS way to remove PFLB control of the assets and systems it does have.
PFLB isn't the only non-influence minor faction to control a system, either - Independent Detention Foundation owns 27, while their superpower counterparts also have a few - again, with no possibility of takeover through the BGS. When the Gnosis is in uninhabited space, Canonn Gnosis Division is the non-influence controlling faction of the system the Gnosis is in.