So...This is another battle of "who can fire first"?
Alright then.
Let's have a look at Enuma Elish:
Fate Extra CCC- Gilgamesh Noble Phantasm Enuma Elish (English Dubbed)-0
After Gil stabs into the ground, the mother of all super-attacks begins to charge itself. He takes the time to monologue for a bit, then unleashes the attack once it's fully charged.
Now let's take a look at one of Calypso's BFRs (skip to 1:44 if the video doesn't do so automatically):
Twisted Metal (2012) Preacher's Cinematics And Ending
Calypso's eyes and body glow a deep red for a split-second before his would-be challenger simply disappears from his vicinity, allowing him to return to his work unimpeded. The victim is next seen in a castle's prison located in what's immediately revealed to be another dimension, viewable through a painting on Calypso's wall.
This also proves Calypso is fine with BFRing right off the bat. He is not a fighter. He would rather be rid of you than have you waste his time with a conflict.
But even without that, it's likely he would do so anyway, as it's one of his most common methods of screwing people over when they make their wishes.
Outside of the above clip, he has also been shown sending people into space (he won't do that here for obvious reasons), teleporting Sweet Tooth into a coffin underground, transporting Dollface to a distant airport runway, and sending Marcus Kane to a mental asylum.
EDIT: I got the living hell ninja'd out of me.
