Not if the fan blows against the dart hard enough. It will end up slowing down, and taking a very long time.
Considering how light the darts are, the air current from the fan will be plenty to keep it in the tube long enough to cool.
If you are going to have it do the gluing itself, why not use something like plastic dip or something? Just an idea, let me know if it's not a good one, but don't flame.
Maybe if you link to what you're talking about we'd have more of an idea if it's a good thought or not.
I've personally never heard of "Plastic Dip" and would be interested in hearing more.
And telling people not to flame is just an invitation for people to pick on you, it's not a good idea.
This will probably be the start of mass producing darts. How hot will the glue be when it hits the dart if it is high temp I would do what zaphodB said into a current of water to cool and not get glued to the bag.
I can only imagine how much trouble THAT would be.
It would be easier to setup a refrigeration unit that cools the output tube itself than to setup a flowing water cooling system. Not to mention the idea of wet darts just makes me twitch.
I'd be using the equivalent of a 10w hot glue gun in the form of a glue-pot, so the glue would be just about at its flow point and not much higher. My goal would be to get the glue just hot enough to form the dome but not hot enough to require excessive cool time. That's part of why I'd like to use a pot instead of a gun, easier to control heat levels and much easier for flow control.
That's also why I want the pause before the dart drops. I want the tip to have a little time to harden before the drop.