The evaporated formic acid crosses the wax-lids of the cells and dissolves in the honey.
The consequence is an increased formic-acid-concentration inside the honey which is not dangerous but can maybe be tasted. It takes 3 months after the treatment for the acid to evaporate out of the hive, including out of the honey.
This is one reason, that the scientists allow the treatment only after the harvest. If the bees eat the acid-enhanced honey in late autumn/spring, it is not dangerous for them at all. But we would not sell it as food for humans.
The other reason is, that the young bees in spring are more sensible to the acid. But, we recommend to treat swarms, as they do not collect honey for us in the first year anyway.