at times, maybe.
You can definitely exert motor torque and braking torque at the same time. You get one of those doo-doo-doo squawks, but you can do it if you don't want to roll backwards on a hill or something.
There might be limits on how long you can do it or how much motor torque you can get, but the electronics don't make them completely mutually exclusive.
If the electronics did make it so there was no motor torque with both pedals pressed, I would guess that would be useful at a drag strip:
Floor the brake. Slowly press the go pedal. Ignore the squawk. Hope that a motor/brake interlock engages to electronically disable the motor torque. Floor the go pedal. When the light turns green, release the brake. When the interlock disengages, the go pedal is already floored. The electronic interlock probably disengages faster than a human can press a pedal.
not sure if it would matter, though: it wouldn't surprise me if a human can go from not pushing the pedal to fully pressing it in under 0.1 seconds.
One nice thing about Model S is that you can turn off creep so the car doesn't start to move until you're in the process of stomping the accelerator.