Without winning the CT, or a boost in RPI, the likely anwser is no.
Charleston may drop your RPI, and from looking at your conference, you may not get a boost by winning a couple of games in the CT. Some of the factors that may come to play in the bubble discussion- How many shock winners get their CT's? If 5 or 6 teams below an RPI of 60 win their CTs, you have no hope.
Factors the sim looks at to get into the CT: RPI (62), non conf (8-2), last 10 (8-2 assuming you don't win the CT), vs top 50 RPI (1-1 now, but the win was against #50 so they could drop to 51), vs. top 51-100 RPI, vs. 101-200, and 200+ (bad loss group- which you have one right now).
As for prestige- a PI final four is equal to a first round exit in the NT.