We’d love to do more testing on this in the future, but our intuition and meat fiber anatomy suggests that no, excess moisture would not be squeezed out of the meat — but only if you don’t overcook the steak. Why?
As noted in On Food & Cooking, most water is "bound" within the proteins, which have to be cooked or "denatured" enough (with higher temperatures and time) before they release bound water, which is what starts leaking from cooked meat.
When a steak, pressing it down might achieve the desired color faster than without a press. This means you’ll likely retain more bound water in the meat, as the steak is in the pan for a shorter time, reducing the risk of overcooking and water loss.
Bigger picture: When cooking, consider which fundamentals have the biggest impact on the final product. For steak, juiciness is primarily determined by the final cooking temperature, followed by other factors and techniques. So as long as you don’t go over temp, squeeze away!
