Yes and no.
Cell phones cannot directly interfere with the wireless link between your mic transmitter and receiver, because they are in different frequency bands and your mic receiver filters it out. However,
cell phones CAN inject noise into your mic lines and cause beeping in your
system. Because of this, we usually lie to the audience and tell them that their
cell phone "will interfere with the wireless microphones used in this production."
Professional shows do not have access to any frequencies that we do not have access to - they simply plan their
system out better and use better equipment (read: more expensive equipment). They also, as Foxinabox said, sometimes have two transmitters on a person to minimize the risk of losing the mic.
Examples of wireless systems used in high-end professional shows include Lectrosonics Digital Hybrid Wireless systems and the
Sennheiser 5000 series systems.