It's a three level process...
US will exist, at least on paper, until a single operating certificate is in place but that's just FAA housekeeping - until all the training/policies are done and the same, the FAA won't let US crews, maint, etc operate AA planes and vice versa. For the US/HP merger that was a year - I didn't pay close enough attention to either the DL/NW or UA/CO mergers to know how long those took to get a single ops cert but between making manuals/policies/procedures identical and training it would be hard to do it in less than a year. This is really separate from *A/OW, just as UA/US are separate carriers in the same alliance.
As a practical matter US will exist, as far as the clearing house is concerned, until at least all open transactions are settled. Nothing says that "new" AA couldn't pay/cash the clearing house transactions. Again, this is separate from *A/OW - "new" AA/US could just code share with each other, missing only the OW/*A connections that would allow US to be a OW partner.
Practically speaking, I doubt that US would move from *A to OW in less than 6 months. I seriously doubt that US IT could make the res/FFer transition that quick. Before that I expect that there'll be a blanket code share which allows US FFers to earn miles on "new" AA and vice versa.