This YouTube video shows that if you fill all 30 of your Boxes and attempt to catch an optional Pokemon, it will display a message saying your PC Boxes are full.
If you catch Xerneas/Yveltal (which are required to complete the game) with full Boxes, a new Box 31 will appear. This Box is only unlockable if you've filled your other 30 and are required to catch a Pokemon to proceed with the story. Because you need to accept a Kanto starter from Professor Sycamore to proceed, it's safe to assume that Box 31 will also appear if you have no room for a Kanto starter.