Dropping the pressure gives you a greater/larger contact patch with the ground. To illustrate this, take your bike out into the dirt. With your tires at 80psi, place your bike in the dirt, then pick it up. See how small the contact patch is? One row of knobs, probably. Now, drop the pressure. See how the contact patch increases? So your tire will be grippier with lower pressure, allowing you to be more agressive with cornering and on loose stuff.

So, to answer the original question, if you can go into a turn with more speed and not bobble because you're sliding around, you'll be able to come out of the turn with more speed.