No. The framework would only run on their GPUs. However, you could have one of their cards in the system to do purely physics calculations, and then use a competitor's card to do the actual display and 3d rendering. They've now disabled this, so if your monitors are connected to, say, and ATI card, you can no longer use the Nvidia card in your system for physics processing.
Before you discount this as an unlikely scenario, consider motherboards with onboard NVidia chipsets. These are usually underpowered for full time duty, but are perfectly suited to being used for physics calculations while a more powerful ATI card in the PCI-E slot does the graphics rendering. This is actually a fairly likely setup these days, and NVidia has just said they're going to block it.
Personally, I agree with others who have pointed out this must be an anti-trust issue. Intel and Microsoft have both been fined heavily recently for doing exactly this kind of anti-competitive behaviour.