No idea, but if you tell us the journey, we can answer!
OK looks like an answer may not be forthcoming promptly, so I will give a more detailed answer:
If your journey has a higher default fare which assumes travel via Zone 1, but it's possible to avoid Zone 1 by interchanging at a station with a pink reader, then yes you will almost certainly benefit by touching the pink reader.
A comprehensive answer for your journey can be provided, if we are informed of the origin/destination.