First thing, aftermarket LDS will not fit in an ADM housing, you need a completely new rear end.
Now, back to your question
No, changing centres (eg changing to LSD) will not affect your speedo. Changing your diff gears will. For example, the ADM S type diff comes with a 3.9:1 ratio, and I changed my ratio to 4.3:1. This is a change of 10%, meaning my speedo is 10% out (eg 50k speed limit = 55k on speedo, 110k speed limit = 121k on speedo.
If you want to get it adjusted, take it to an auto instruments guy, and they will most likely install a "reduction" box on the gearbox output, or re-calibrate the speedo (or both)