I recently bought a Z440 workstation with integrated Quadro K2200 GPU
The graphics card in your machine is not an integrated card so there is no problem to remove it and replace it with a new card. 
For my needs i would have removed the Quadro card and replaced it with the Titan X card. If you do need a Quadro card for the software you use i am not really sure if those two card can co-exist or not. If my memory serves me well it´s not possible to mix a Quadro with a GTX card. As have been pointed out there will most likely be a driver issue.
Maybe some one from HP can chime in!