No. they won't, because with her being a private citizen, she won't be subject to the ethics complaints tied to her office, so she won't be costing the taxpayers of AK money in fighting them.
It has nothing to do with the use of her TIME as Gov., it was simply the fact of her existing, that caused the folks to file complaints.
Yes, the ethics complaints were a problem, but at least finish her first term. That's what Reagan and Bush would have done under the circumstances.
Quitting, at this point, wasn't the answer.