Does frame size inside a particular model affect the ride characteristics of the bike?
The idea here is that a frame is typically originally designed in a 56cm frame, or the equivalent median size for the "average size" rider.

When the frame design is tested and finalized, most manufacturers minimize the changes they make when creating the molds for additional sizes. 

This can result in small sizes having a harsher ride than the median, and large sizes having a softer feel, and slightly less power transfer. This is accentuated by the fact that most riders on a small frame have less weight and mass with which to flex the frame, and larger riders have more. 

Really high quality manufacturers, like Storck bikes, for instance, use progressively shaped and manufactured tubing, which allows for the ride on the smallest frames and the largest frames to have the same ride characteristics of the median original design. 

I am not personally familiar with the manufacturing techniques of Pinarello bikes, but their unique frame and tubing shapes would indicate to me that they would need to design each size independently, which would give a consistent ride characteristic, regardless of size. 

Pinarello is known for the stability of their ride, but also for having a heavier than average frame weight. A 56cm frame is typically around 1800 grams, while the Scott Foil or the Storck Fascenario 0.7 G2 are 1050 grams and 1200 grams respectively. 

It is more important that the ride characteristics match what you want from the bike, than how much it weighs, of course. 

Have you ridden and been fitted on the bike you plan to buy? If not, do so first. 
(Full disclosure: I manage a shop which sells Storck. This is not an ad, but it is why I'm familiar with the topic.)