Yes it can. There's a good way to go about setting the witness point when changing strings. Assuming the saddles were in the correct position with the old strings, move the saddle further back before you install the new strings. After installing the new strings, tune up and set the witness points. Check the intonation - it should be slightly flat at the twelfth fret. Move the saddle forward a bit, set the witness point again and retune. Check the intonation. Repeat until the string is intonated properly.
The reason you want to move the saddle back in the first place is because setting the witness point puts a bend in the string at the saddle crown. Then as you move the saddle forward during intonation, the first kink will be behind the saddle and not in the speaking length of the string. It's a safety move to ensure that you don't put a kink in the string where it is vibrating. The critical bend will be just at the saddle crown.
Is that clear? I'm not sure I explained it well.