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You are correct that if both cards use the same video driver you will be OK. And, if nVidia's site has you downloading the same file to install the driver with, yes it will be the same physical driver.
For the record,, I had a Quadro FX1700 on my system, and I added a GTX 580, udpated the drivers and voila!.
Now, the only thing you have to be careful is that Premiere (and other software) seems to use by default the first card listed in the system (so your premiere perfrmance might be affected and you might think adding a better GPU didnt do anything for you because premiere only use one GPU for CUDA and it will try to use the first one on the system),, so, on the Nvidia Control Panel, under Manage 3D Settings, make sure that you are using the right GPU for CUDA with premierepro.exe (dont select "ALL", but force the good one instead)
It happened to me,, save yourself about an hour of frustration.
Thanks for info! I will try the 8400GS and tell you how/if it works.