From what I've learned I agree with your statement that "I would think the Botox would wear off whether you were talking or not talking." I have a job with very little voice requirements (i.e., computer work) and my botox injections wear off regardless. Granted if you talk and/or act all day you might feel exhausted from it (beyond what someone without SD would feel) but I wouldn't worry about it too much unless that bothers you personally. While talking all day (for me, personally) would exhaust me and drive me nuts... silence all day does little (if anything) to help my voice.

Personally, I doubt pitch changes have anything to do with how long botox lasts.