Can I install drywall or wall board right up against the gas vent?

No. Drywall and wallboard are considered combustible materials and should not be installed against the vent including the use of this material to close off the hole around the vent. Type B Gas Vent requires a minimum of one-inch clearance to combustibles. This one-inch is a typical clearance for all brands of Type B Vent, but each section of vent pipe is marked with the clearance required by Underwriter Laboratories, so it should be checked.