When TKD was first published, it contained the word ghargh, translated serpent, worm. Notice that comma; it's important. The food known as gagh hadn't been invented for the screen yet.
When working on the episode of [i]Star Trek: The Next Generation[/i] when Riker serves aboard a Klingon ship, the writers invented this food and seem to have looked up some stuff in the dictionary. They came upon ghargh. And then the actors proceeded to butcher the pronunciation, making it sound like gaH (notice the g). Scripts and fans decided to spell this as gagh. And someone starts calling it serpent worms, completely ignoring that comma and inventing a new thing.
Okrand, when writing the second edition of the dictionary, was incorporating all (most) of the Klingon that had appeared on screen since the first edition had been published. He took the actors' pronunciation of ghargh as gaH, assumed that first sound was q (because it sure as heck wasn't gh), and invented the word qaH. This word represents what ghargh become after prepared as a dish.
So it's not that gagh is English; it's that it's a common way to write Klingon qagh based on the mispronunciation of actors, and it gets translated as serpent worms due to a misreading of the dictionary.
I don't think anybody has an answer for that.
It could be that the first English speakers who came across the word heard it as "gagh" - the closest they could get to writing down what they heard using English letters.
Perhaps the first Klingons they met spoke a dialect where [q] is pronounced differently from in Standard Klingon.
I don't think anybody knows the answer. It's just the conventional English spelling of the term.