No, not until January

after many rounds of frivolous law suits if I'm reading the tea leaves correctly

The lawsuits won't stop people from taking office.

The newly elected Congress critters can't take office until they are sworn in by they speaker. As we've already seen from the pettiness of the current Squeaker of the House Mike Johnson, he has already used skullduggery to delay the swearing in of new members. I'm sure claiming that a seat's validity being questioned by ongoing litigation would be cause to delay that person being sworn in.

Over the years I've seen way way too many off-by-one errors when people reflect on who was "in charge" at the time.