Yes, knowing what scope it is might be helpful. This is actually more common than people might think. With a SFP scope it's more a matter of how much error will it have, if you measure closely enough. It may be .01 MOA, .1 MOA or 1 MOA if anything is out of alignment just a little bit. Naturally higher quality scopes will tend to be closer to the first number, cheaper SFP scopes may end up toward the last number or worse.
Keep in mind with a SFP scope, even if perfect, it will only be the very center of the reticle that stays in the same place--the entire rest of the reticle will move relative to the target when the scope is zoomed which will be obvious with any holdover points, mildots, etc. If you want to use the scope on different powers you can only use the very center of the reticle (unless you do the required math, of course).
None of the above applies to FFP scopes. The reticle moving relative to the target with zoom is physically impossible with FFP scopes. The entire reticle will remain constant so holdover points as well are usable on any power.