Does the Sphere L22 microphone have a flat frequency response?

No. The L22 microphone is designed to have an on-axis and off-axis frequency response that is most amenable to modeling other large diaphragm condenser microphones, with particular attention made toward modeling the U47. Because of this the L22 microphone also is an excellent sounding microphone even without using any modeling. The frequency response is also designed to be very consistent from mic to mic, so that the modeling is accurate.

Also, keep in mind that because of proximity effect it's not physically possible to make a directional microphone that is flat, except at a single distance (NOTE: Variable-D microphones, such as the Electro-Voice RE20, reduce proximity effect and are more consistent at a wider range of distances, but nonetheless proximity effect is still a significant factor). But using the "Sphere Linear" model with Off-Axis Correction enabled it becomes possible to have a directional microphone with a flat frequency response at any user selected distance.