Can I use the Sphere plug-in on material recorded with some other microphone?

While there is nothing stopping you from doing that, the results will most likely be extremely poor. The Sphere microphone is specifically designed and calibrated to work with the plug-in. There are very tight tolerances on frequency response and polar response of the Sphere L22 microphone, so that the modeling is consistent from mic to mic. But even more importantly, the microphone is dual-channel, which encodes the directional information for the plug-in which would be entirely lost with a single channel microphone.