Quick Answer: You can absolutely press tofu overnight or well in advance. In fact, it's probably the best way to do it so you're not waiting around while the water is draining out.
But, there are a few things that you'll probably want to know about doing it so that you don't make a mess or of your fridge or your tofu.
You Need the Right Press
If you look at all of the tofu pressers out there, then you'll see that most of them probably aren't well suited to handle pressing tofu overnight.
Why? Because you don't want to leave tofu outside of the refrigerator or the freezer for a long period of time or it will go bed.
But there is one option...
If you look at my guide to the best tofu press, you'll see that first pick (the Tofuture) is specifically designed to handle overnight tofu pressing. It's the only one on the market that I know of that seals off the block and catches all the water. A great option if you're going to be prepping a lot in advance.
You can certainly use some of the other models, but you'll have to have something to catch the water in the fridge. It also won't be sealed inside the fridge so it may absorb some other flavors and smells.
Keep It Refrigerated
You don't want to leave your tofu out on the counter all day while it's pressing and draining. Sure, an hour or two is fine, but too long in advance and the tofu might go bad.
That's why I highly stress the recommendation above if you're planning on doing it in advance. It's best suited for the refrigerator.
You can totally press your tofu to get the water out and then freeze it. You can even do the process vice-versa.
Freezing crystallizes the water molecules inside the block which makes it have more holes. Subsequently, it makes the draining and drying process easier because the water isn't "stuck" inside the tofu.
Obviously, the less water you have in the tofu to begin with the less of an impact this will make.
But either way, freezing it before or after pressing is a great way to prep in advance.