I am installing a Honeywell T841 onto existing RGYW wiring. The fan kicks on, but I notice the air conditioner is not running. Were one or more of these supposed to go on the W2 or B terminals? Thanks!

Need to have more numbers in model number to be sure There's about 30 T841 t'stats and some are1, 2, and 3 stage heat pump and some 1, 2, and 3stage AC.
If you have
R to transformer
G to fan relay
Y to contactor in outdoor unit
W to Gas valve
You have the thermostat wired right.
Depending on the T'stat B could be the common side of the transformer or 2nd stage heat.
W2 terminal are for 2nd stage heat
You need to put the thermostat on cool and lower the setting to bring on the cooling. Then go outside and see if you have power to the outdoor unit and 24 volts to the contactor coil.