Yes, you can park for free. You should be able to pass through the parking gate as well for free as long as you have a PS/ADR. Just got to the resort gate(far right) and tell them you have a PS for breakfast. They may have a list to check and make sure you have an PS/ADR. We have never had issues doing this for dinner at Ohana but it may be different for breakfast since many people will try and park at a hotel to go to the MK.
Once you get to the Poly they will give you a parking pass that will be valid for 2-3 hours usually.