Will it be useful to keep my old video card in my computer?

There's no "technical" limitation to this as Windows will ask which card is the primary one and will use that for all intents and purposes unless you tell it otherwise through Nvidia's control panel.

However, I don't see the point of keeping an old card that will just contribute to heat and power draw of your system. Dust can be reduced by covering the hole in the case (if you have one), but even older GTS cards do produce quite a bit of heat. Also, there's no purpose (as noted in the comments) to having a "dedicated" PhysX card since the high-end cards nowadays will out-perform them while being more energy and heat efficient.

Your new GPU will handle everything, rendering your old GPU pretty much useless. In addition to extra power usage, not to mention which will generate heat, there is another issue regarding PCI-Express x16: If your motherboard have shared PCIe x16, when you install two GPUs, each will use 8 lanes instead of 16, which will reduce the performance of your primary GPU. There is not much point in keeping the old GPU in the system.

In fact it could be useful to have two GPU in system but only if you are interested in GPGPU. With one card it's impossible to debug CUDA kernels because when you create break point in graphic computation you will hang your UI (although latest NVidia cards support debugging on one device)

I used to have 2 GPUs in the system and I use one for computation and second for display UI. This allow me to use all avaliable memory and create proper benchmark results.