Algebraically it is not important -- as long as you adjust your transfer functions appropriately. In practice, with floating point round-off and limited range, there could be some effects, which could be anywhere from minor to major, depending on your transfer functions.
Normalizing makes it a lot easier to compare the effects of different parameters. If A varies twice as much as B, is that because A is more important in determining the correlation, or is it because the range of A is higher and maybe A is actually less important? When you normalize then you do not have to think as much about how to interpret the results.