I've used this service once (for The Last Ship) and they did not check ID. I highly doubt that box office attendants are aware of how you purchased your ticket if you're just picking up. The only exception is probably the Vivian Beaumont where they have their own student ticket program.
You probably won't even get an approved membership. There is no age range to this program; but rather they take your name and institution information and literally confirm your name within the registrar in which you are enrolled. Your issue will be getting your membership approved.
I've been asked for id at some box offices and not at others. as I remember neither the circle in the square nor the music box asked for id. As it was mentioned before you will have trouble getting membership. My brother was denied because he had a balance on his term bill.
I wasn't checked for ID when I went to see Les Miserables, but they did check my ID at Hedwig and Hand To God when I purchased tickets through Tix 4 Students. The stickler with the system is your membership needs to be approved in order to use their services, and the way they do that is, upon registration, I believe they ask for your full name, the institution in which you are enrolled, and the last four digits of your social security number so they can confirm your enrollment with that institution before approving your membership. The site doesn't discriminate against certain ages because people of all ages are attending college.
"Mostly, I loved the size of these people's emotions. Nobody has emotions this size anymore. Outsized emotions. Operatic emotions. Kushemski and Vanda are like Tristan and Isolde, they're Paolo and Francesca. Nobody's in total thrall like this anymore. Nobody's overcome by passion like this, or goes through this kind of rage." Thomas, Venus in Fur
Shows on Telecharge are supposed to ask for ID and shows on Ticketmaster are supposed to not have to ask. You will see on the site Telecharge shows state in the info section that you must show ID and Ticketmaster shows do not say that. You can actually even print e-tickets for Ticketmaster shows, but not Telecharge shows.
This is because the way the site works is you use your unique member code to purchase tickets on Ticketmaster, but through Telecharge it is actually using an exclusive discount code to purchase the tickets, which can be used by anyone who obtains the code and is why they need to verify that purchasers are actually students at the box office.