Yes, but that just adds an unnecessary extra step.
It seems redundant since Flame bows exist, but I can support it regardless. It's a cheaper alternative, that's for sure. The one change I'd recommend is giving them a cooldown like Ender Pearls but shorter so somebody can't spam them and set a whole group on fire in under two seconds.
Good point; I forgot to consider that. I'm thinking 0.25 to 0.5 seconds would be s reasonable cooldown.