First of all that is not how a mil-dot reticle is designed to be used. But let's say that is the way you want to use it and you construct a range table and it just so happens that your center CH is zeroed at 100 and it turns out the first mil-dot down is zeroed at 200, the second at 300, and the third at 400, then if it it a first focal plane cross hair (reticle enlarges as does the target as you increase power) then no, your zero with the lower dots will not change. But if you did that with a second focal plane (target enlarges but cross hairs stay the same size) then yes, your zero would change with the lower aiming points and would only be accurate at the particular power at which you constructed your range table.
Mil-dots are used for range finding and judging where to hold off at long range and where to hold off due to wind, not to sight in where the center is zero at 100, first dot down is 150, second dot 200... For that type of use it is better to use a reticle set up for that purpose. The mil-dot is not intended to work for the application you described.
The type of reticle and use you are talking about is an excellent example of the Leupold Long Range reticle, where you have two dots below the cross hair, then you do use them as alternate zeros for longer range. Zero the main CH at any power but use the ranging dots only on the highest power setting.
It is set up to zero the cross hair at 200 then the first dot below the cross hair is zeroed for 300 and the second is for 400. This can vary slightly from cartridge to cartridge so you must verify by live fire but the system ONLY works on the scopes highest power setting.
Here is a
link as to how the Leupold LR reticle works.
A lot of people like mil-dots for the sake of the way it sounds but have no idea on how to actually use it. The mil-dot works for any caliber or any velocity weapon but you must know your particular zero and trajectory, whereas the multiple zero reticles only work within a certain velocity range and if you round falls outside that range you have to construct your own ballistic table.
Books have been written on how to properly use the mil-dot and it is too involved to explain in a thread. The best bet is to download a manual on mil-dot use and read it.
A short answer is first you use the mil-dots to determine range, then knowing the trajectory of your rifle you use the mil-dots again to judge hold over and windage. For a first focal plane reticle it works at any power. For a second focal plane it works only at one power, usually 10X.
Here is a
link that tells you how to use a mil-dot. It sounds complicated but once you get use to it one can use it very quickly and as I said, .22 LR or .50 BMG, it works the same.