Very likely.
Many dictionaries use the spelling “hoosegow”, which is weird. That seems to be a British spelling, but the word is definitely an Americanism.
Maybe related to “porridge” as a slang term for imprisonment? Or the crank handle hard labour prisoners had to turn so many times a day?
“23 years later”
I mean, good grief!
That’s what I would have guessed too, but according to Eric Partridge it may be the other way around. Re: stir
An abbreviation of Romany stardo, ‘imprisoned’, ot more likely staripen, loosely stariben or sturiben, a prison.
(A Dictionary of Underworld Slang.)
In The Concise Dictionary Of Slang he says of porridge
Perhaps suggested, in part at least, by the semantics of S.E. stir, by a pun on stir, a prison.
And that’s what we have Eric Partridge for.
j