Several (IRL) days after placing a marker sign for a beehive I returned and completed construction. I also built 4 other hives 5 squares away from each other. The next (in-game) day I returned to see the yield, and gathered 38 honey from the first hive. The other four hives yielded one honey apiece.
I can only assume the unbuilt hive gathered honey the entire time it was a signpost, as I do not believe there is any way it could accumulate that much honey in one game day.