Gas dryer water heater vent
NO
Dryers need separate ventilation because lint gets into their ventilation system and builds up there -- in a shared vent, this'd cause excess backpressure that the water heater can't tolerate, leading to backdrafting, CO, and an unexpected visit to the ER.  Furthermore, a gas dryer is a forced draft appliance, which aggravates the backdrafting issue and will send you to the hospital with the CO detector ringing in your ears well before lint buildup will.
Atop that, Section M1502.2 of the International Residential Code prohibits what you are asking about:

M1502.2 Independent Exhaust Systems
Dryer exhaust systems shall be independent of all other systems and shall convey the moisture to the outdoors.