Will a wick-type heat pipe still work if the hot side is at the top and the cold side is at the bottom?
Yes it will work well. Usually wick type heat pipe used when condensation zone is below the evaporation zone. Wick use capillary action as its principle of movement, so heat pipes are often used in space application where, at zero gravity a wick has to be used. Where possible, under normal gravity, heat pipe heat exchangers (thermosyphon) should be operated with the condensation zone above the evaporation zone when the need for a wick can usually be avoided.