Yes, the largest reason for server-side lag is because of the large number of people online.
No, graphics dont exactly cause lag, but the large number of graphics that are downloaded to your device can slow down the app. In that respect, 1k hats have nothing to do with it; its the custom heads. The last time I looked into my iPhone, there were over 15,000 head files, compared to about 300-500 images in each shield/sword/hat/body folder.