My understanding is that it is internal rail industry policy to accept tickets interchangeably between Haymarket/Waverley.
So I am pretty sure this discussion is moot!
I would be extremely surprised if you were not allowed to exit. Indeed, it's quite possible that the ticket will open the barriers, so you may not need to interact with staff.
However, for completeness, and this would work for other situations where such easements are not in place, you could potentially book an e-ticket from Waverley to Haymarket (£2.80 for a flexible fare, but I found advances for £1.20)
If staff refuse to allow the original fare to be finished short, then you can use the additional ticket to exit, and you've only lost out by a small amount.
Your journey would nominally be Manchester - Haymarket - Waverley - Haymarket, and you would have paid the correct amount for such a journey, and it would be ludicrous for someone to argue that you should have actually made the double-back to Waverley.
If the original fare is accepted, and the additional fare remains completely unused, you could get a refund on it (some sites won't charge an admin fee, for example we won't charge an admin fee providing it's within 2 hours of purchase)