No. Zak Bagans does not have cancer. He has made comments about cancer in reference to a fan, Lauren Skillman, that died in November 2011.
Bagans, more precisely may be suffering from breathing issues (could be asthma or bronchitis as what sources suggest).
Many viewers have asked why he wears gas mask/respirator sometimes during investigations. He's protecting his body from potentially toxic mold, carcinogenic asbestos dust, and poisonous lead paint dust.
Wandering around old abandoned buildings has weakened his respiratory system, leaving him sensitive to airborne impurities and particulates.
Zak Bagans created the show Ghost Adventures with Nick Groff, it premiered in 2008. They travel the spooky back-roads researching reports of paranormal activity.