@Sepulchure It is most definitely possible–if not probable–that they will discover this fact.
When I worked in admissions, the Ivy Group universities along with MIT and Stanford most definitely DID exchange lists of students applying and admitted under Early Decision/EA. The Ivy Group admissions policy clearly states that violating a “early decision contract” is grounds for rescinding an offer or rejecting an applicant. To my knowledge, this is still enforced.