Uverse is fiber to the curb and then copper to nid. Then usually they run it either coax or Ethernet into your house, I think a lot of times they will just use the existing coax because it's easier. However, I don't see why cox and U-verse can't co-exist. I would just give them specific instructions not to mess with it and inform the installer when they get there they need to run separate coax lines or Ethernet for U-verse, that you want to keep your cox intact. I would also double check to make sure cox is still working before they leave.