No, it will not work well. Like you said, the EOTech is designed for a flat top AR, and will sit way too high to get a proper position on the M1A.
A much better setup is to replace the factory scout mount with an Ultimak mount, which sits lower, and then mount either a 30mm Aimpoint in a low ring, or an Aimpoint Micro in a low picatinny base. Either one will give you co-witness with the iron sights.