As others said, it doesn't affect titling at all. Some dogs take to it just fine, others don't. When I was injured a couple of months ago, I tried to have a few people run Meg in class, and it was a mess. I wound up having one friend who could get her to run, and she did do several classes at the trial that week. I couldn't be anywhere in her sight from the time she left the crate until she was done the course.
Gusto will be learning from an early age to work for anyone! It is a skill I want him to have, whether I ever need it or not.
And yes, the one class I ran (hobbling all the way) that weekend was the run we needed for our PDCH. Nobody but me was getting that!