Of course they do. It's a fact of life.

Yes I have, and I will again!

Even the strongest or most intimidating beings need love and affection with hugs, they feel protected and warm but more than anything safe and it is the little ones who most want to hug their gods and even more so if they are their favorite pets that stand out for being the most devoted and better protected from super predators like their gentle masters and protective friends.

No super predator, army or government would want to harm a God's favorite pets, of all of them they are best served by their Predatory Deities. I envy being protected by a Dragon who protects you better but is sadistic with his food, the rest of the world.