Is it possible to get educationally-priced hardware by visiting any given physical Apple Store, or is that only achievable online or at college stores?
Yes, you can get educational discounts at a physical Apple Store -- I have done it, though it has been a while ;-).
They require verification of your status which can generally be done with a student id.
Yes, you can get the educational discount at an Apple Store. Just make sure to bring your student ID.