It is possible. I too had the exact same situation with Americredit. I fell behind on two payments and they took the car. They let me catch up on the payments and pay the fees and I got the car back and continued paying on-time through the end of the note, which ended 3 years ago.
Come this past August, I started to clean my credit. I had the repo reference on all three and 12 lates. I sent GWs several times without any response from Americredit at all. I then looked at the CRs and noticed that on EQ and EX deleted the repo reference completely, but kept the lates. TU kept the repo reference but deleted the lates, all of them. I'm sending a new round of GWs but they seem very workable, though lacking any input.