But I recommend doing so, for several reasons. One is that the boot simply will perform better. Gore-Tex is funny stuff. True, it's waterproof, but the physics get complicated. If its surface gets waterlogged, for instance, it has a more difficult time transferring water vapor out. When the outer layer is cool and damp, that may cause condensation on the inner layer when warm, moist air hits the cold Gore-Tex. So anything you can do to keep moisture away from the Gore-Tex will aid its performance. Beyond that, treating the leather with something like Nikwax Aqueous Wax ($7.50) will keep it in better condition and help it last longer.
The wild card is whether your boots have a one-piece all-leather outer, or are pieced together from various bits of leather and fabric. If so, then the seams are difficult to fully waterproof. What might be helpful is spray-on leather treatment, such as Tectron Extreme ($5.50).
Along with all the above, take steps to keep the boot clean and free of sweat and grit. Brush the exterior off when it gets dirty, and occasionally scrub the exterior (gently) under warm tap water. Rinse out the inside of your boot as well, as that will remove acidic sweat residue. Dry at room temperature, then treat with dab- or spray-on waterproofer.
Nikwax can be found from REI here.