+1. Below a certain temperature, I think the heat loss would make an alcohol stove unable to boil water. That said, a creative setup using lightweight insulation could possibly turn that around.

YMMV, but I don't care to use an alcohol (methanol) stove unless the cup/pot has a tight fitting lid. In my few modest experiments, I always got a hint of unburned alcohol in the flue gases, and its affinity for water may not improve the quality of the tea...