Digging up a diamond blocks the drill but the diamond isn't spawned. Picking up the drill or the furnace doesn't yield any diamond which was dug up.
Does this count as a bug or shouldn't be directly inputting to begin with?

you should only drill up diamonds from coal if you turn on the gems from other ores option.
and if it is enabled, yes, it would lock up if feeding directly into a furnace, since diamonds can't be inserted into the furnace.
If you intend to fuel a furnace in this way, I'd recommend turning off the gems from other ores option.