No...Not necessarily. It depends on other variables like barrel contour, height of scope base(s) and perhaps even the true outside diameter of the front objective ( some have very thick material around the front objective lens) as well.
All of my 56mm front objective scopes have 1" rings. I did have to use 1.25" rings for a scope with a 60mm front objective.
56mm front objective...NightForce 20 moa extended one piece base with Badger Mx 50 1.0" ( Their "High" rings ) with a heavy contour...almost MTU barrel. On a Remington action.
This is another scope...same kind as above...with the same Badger rings....but on this rifle...I have a Ken Farrell 20 moa one piece base. This rifle has a very similar contoured barrel as the above rifle but there is even more space between the objective and barrel. So, the thickness of the base is one variable coming into play.
This scope has a 56mm front objective but the material around it is thinner. This is on a Remington action with 1" high Seekins rings and a one piece 20 moa NightForce base. The rifle barrel is a heavy Palma contour. It is the slimmest barrel I have and consequently this rifle has the largest gap between the front objective and the barrel.
Last picture...a third brand of scope with a 56mm front objective, Ken Farrell one piece 20 moa base and 1" Farrell rings on a rifle with a Krieger MTU contoured barrel. Probably has the least amount of space between the objective and barrel.
So...there are variables other than just the front objective....that need to be taken into account when buying the correct rings. I've gone with all 1" high for mine....so I can swap scopes from rifle to rifle, if need be, and I know there won't be an issue. Even if I swap to a straight cylinder barrel.....I should have clearance.
Here's a handy little calculator that might be of help:
http://www.mil-rad.com/scope_ring_calculator
Wayne