Yes
There is nothing the GM cannot do with their NPCs which players can do with their PCs, as far as gameplay actions go, so, declaring details in the middle of the action isn't off the table. And there's no reason the GM wouldn't spend the Fate point for it.
To quote Declare a Story Detail on FC p. 13: "To do this, you’ll spend a fate point."
However, since the GM is the referee of the acceptability of detail declarations, and story detail declarations "work to your character's advantage" by definition (FC p. 13), it begs the question of whether this is a good idea or not. I, as a GM, would make very sure to pay attention to the explicit reference to "player buy-in" which is also spelled out on page 13, because holding the veto power over my own NPC's play options can easily create perceptions of unfairness.
It's not a big thing. It's just a Fate point. As a GM, I don't spend a lot of NPC Fate points anyway, myself. Since I get them every scene, I can already get way more than the players do just by changing scenes a lot. So it pays to be fair here.