Disinclined: unwilling; reluctant.
to: you should know this word.
Acquiesce: "accept something reluctantly but without protest."
So: "(Reluctant) to (accept something reluctantly but without protest)."
Eliminate the double negatives: "Reluctant to accept something reluctantly but without protest."
Result: "To accept something but with protest"
AKA "I'll do it but I'm going to whine about it"
I don't think it works that way. Acquiesce is accepting with certain added context, reversing it means "not accepting" it doesn't reverse the context.
As a whole, it literally means "I don't want to do this thing." It doesn't say you absolutely won't, but it doesn't say you will. However the actual explanation of it meaning "no" points to it being an overly polite and roundabout method of refusal. Basically it equates to saying "I'd rather not".