Would need to build some new modules to replace at least Zarya and add some power. In addition they have been using Progress for reboosting, though it has been demonstrated using a Cygnus.
It could be done, but folks would need to get going pretty soon. My understanding is Rogozin said they would take their modules at the closing date. Don;t know how gentle that process would be.
My understanding is that NASA has had plans for a while for private stations to replace the ISS function, and they would need to accelerate those. If so, NASA would probably prefer an orbital inclination less than the 53 degrees the ISS is currently on, an awkward inclination that was specifically done because Soyuz would not be able to get to that orbit from Baikonur.