I'm sure the answer is either 'yes' or 'no', depending on the circumstances.
My only experience with recovering a cab required me to scrape, chip, and sand - because the remaining glue from the initial covering was attached sporadically and was quite bumpy. Applying fresh glue without cleaning would have resulted in an unattractive surface. Could I have 're-wetted' the glue with fresh contact cement? Probably depends on the original formula, and who knows how much time. And I might have been tempted if the original application of glue had remained in a consistent layer. As it was, cleaning it all off was easy because the glue was hard and crusty. That's just my mileage. Yours may vary.
I'd suggest "testing a small spot in an inconspicuous area" as they say, to see if the new adhesive plays nice with the old.