I have a friend who also does this part of the training with the puppies, and even though it's socialization, it's still considered part of the training and the dog is afforded the same protections as an 'in training' service dog and she's allowed to take him anywhere. Her dogs are being trained to go into guide dog training programs so they do have a vest and special harness (maybe a muzzle..) and she works with him on behaving around people when he's wearing that vest. So even though he's not training to do his eventual job, he's learning how to be a guide dog.
Yes socialization is still part of the training process. SDiT covers this, not just the "task training".
To OP, just so you have it during the trip here is a link to the Michigan State College of Law website that has a table of all state laws regarding service dogs and SDiT. Texas has changed their law since the table was last updated, that is the only one as far as I know.
http://animallaw.info/articles/State%20Tables/tbusassistanceanimals.htm