Generally no - they will just take your name and look up your name. BUT if there are any problems - like they can't find you - you would do well to have the # and show it to them. So keeping them in your phone is a smart idea.
Take your daily list of conf numbers with you. There have been a few times when they were't able to locate me with the right name. But as soon as I gave them the conf number, I popped up. It would seem that my name had been hugely misspelled or completely different. But, that was before online ADRs could be made, so possibly it isn't as big an issue as in the past.
I still carry mine with me every day...just in case.