The nominations of Saad, Kavanaugh, Myers, Boyle and Haynes are all pending "in the Senate" at this moment. Saad, Haynes and Kavanaugh in Committee, to be precise. Only Kavanaugh had to be "renominated," the others have been pending since February last year.
Does that change your guess to "Yes, Frist will bring them up."? Heck, Myers and Boyle aren't even contentious, best I have been able to recon. And they are out of Committee, currently on the Senate's Executive Calendar, Myers since March last year, and still not brought up for a vote.
All I can do is hope that he will. I think Frist is guided by the NEWS of the day, rather than what needs to get done.