No one answered your question directly, so I will. If you sight in with ammo XX, then shoot something with a different bullet weight and/or velocity.....NO, the rifle will not shoot to the same point of aim. As to HOW MUCH off it will be - that depends - no prediction will be accurate (could be 1", could be 3", etc.).
In addition, .22 rimfire ammo has another built-in conundrum. Standard velocity ammo, which is considered less than 1100 fps.....and high velocity ammo, more than 1100 fps (usually, something over 1200). These will shoot to wildly different points of impact. High velocity rimfire is almost never as accurate as standard velocity, as well.
There is actually a THIRD issue, as well. That is ammo quality, that is, CONSISTENCY. The low quality, cheapo high velocity .22 rimfire ammo will produce fliers all over the place, because it is NOT consistent. High quality, standard velocity .22 rimfire ammo is (relatively) expensive, though still not as expensive as centerfire ammo.
So, combining the different bullet weight issue with the standard vs. high velocity issue, plus the ammo quality issue, makes for a hodge-podge of ammo.....which will vary, in terms of accuracy and point of impact....all over the place.
The only solution - since you can't hand load .22 rimfire - is to experiment and find the ammo YOUR rifle likes best - then STICK with THAT ammo. So, that is what I recommend - STRONGLY. Once you find what your rifle likes, stock up !