We didn't notice any issues with park hours, etc. However, we have been there twice and here are things that happened. The first time: The runners start REALLY early, and we watched them take off from our DGC DTD view window. Then, we took the back stairwell down that empties out by La Brea , and were STUCK in the little grassy area for 45 minutes because the runners were coming out of DCA back into DTD (we finally called a member of our party who had to come dowstairs in her robe to let us back in that door since you can get out, but not back in through it). DTD was pretty off limits druing that time, but I don't think it affected getting to the parks.
The second time, we had just arrived to the resort and there was NO WAY you could get into the GCH by a cab on any street from any direction. Our cab driver asked every policeman and CM about this and we were directed all over the place forever, and finally let out way before the entrance to DLH and had to tote all our stuff through DTD to the Grand. So, I would not arrive during the actual race and you may find some areas unavailable, but going to the park should be fine.