"Let say I have the student pay on the notice without amending the student's return and have parents amend their return to claim the student? Will they disallow the E-filing because the student's Social Security Number was used on another's Primary Return?"

Youd need to allow 4-6 months for processing time on that amended return before you could EF any other return that included him on it.

Im guessing the parents already got the stimulus for the kid as an EIP advance during 2021, he was on their 2019/2020 return, right? I guess you could pick up some educational credits on the parents return if the kid was included.