The only quail I know is Robert from my favorite book 'That Quail, Robert' and the wonderful little flocks of quail that roam our property.
But I do know Robert's human family regularly fed him sugared treats. Not a great idea due to obesity and other health concerns, but he didn't seem to have any observable problems from it.
And I used honey extensively throughout my rooster's recovery process from a coyote attack. I applied thick coats a couple times a day on his wounds. He would dip his beak into the honey and I'm sure consumed a small amount daily for weeks.
In fact it's quite possible his ingestion of honey may have helped with his remarkable healing. I'm not advocating intentionally feeding honey to birds; I'm not clear yet on any harmful side effects. But Henry seems to have handled it without any dire consequences.
I would think the same would hold true for quail, as long as each treat contains a very small amount of honey.