The Nvidia GTX275 and the Nvidia Tesla C1060 have exactly the same compute capability (1.3) number of multiprocessors (30) and CUDA cores (240).
I am wondering if it would be possible, in principle, to use the GTX275 as a GPGPU along with another GPU card (for video output) and if it is possible, then what the would the hardware constraints be. Obviously (?) a less-powerful card would work as a bottleneck to fast video output (e.g., rendering in quasi-realtime). What if I used one GTX 275 as a GPGPU and two GTX275 in SLI tandem with a 1200-watt power supply? The whole rig (used) would cost me less than half the price of a single C1060.
I'm fairly certain that what you suggest would work. However, there may be lower performance due to different GPU architecture, though I doubt that would be the case. One of the only reasons that the Tesla GPUs are so expensive is due to the amount of onboard RAM. The C1060 has 4GB GDDR3 whereas the GTX 275 has 896MB GDDR3. The excessive amounts of RAM are necessary for CAD and stuff like that, where massive models must be loaded into memory. If you're only using the cards for their raw CUDA processing capability, then you should be fine.