Does transferring from one ‘Hidden Ivy’ to another act as an edge in any way?

https://en.wikipedia.org/wiki/Hidden_Ivies

It is a group of colleges considered by the authors of the book to be more-or-less equal to the Ivy League in educational quality.

Some of the names on the list are well-known and respected: Notre Dame, John Hopkins, Stanford, Duke, Georgetown, USC. Many others may surprise some parents/students who are just beginning the college search process: Claremont McKenna, Rochester, Dennison, Richmond, etc.