Good thought, but if he signs up it could just be a diversion. Besides, Todd does not have to be with her 24/7 at that point of the campaign.
Also, him racing would keep talk centered around her/what she was doing at the time. There are all maner of advantages to him running in it or just signing up.
Have a look through Robert Greene’s 48 laws of power. Pretty eye opening experience.
Thanks for the tip. Interesting read.