Can I use Sphere modeling with only one channel of the L22 connected?

The short answer is no. Even though the Sphere L22 microphone can operate as a conventional single channel microphone, the Sphere plug-in's mic modeling is only designed to work with the two channel output of the L22. This is done because Sphere system uses the information provided by the front and rear capsule in order to faithfully produce the frequency-dependent polar pattern behavior of studied microphones.  Once the Sphere plug-in output is printed or committed, one can work with the mono result, just as one would with any conventional microphone.

For more information about why Sphere uses two channels check out the FAQ: Why does the Sphere microphone have two output channels even though I just want to model a mono microphone?