Absolutely! They're always playing (the flute...lol )
God is the greatest enjoyer. Krishna I think most represents living to the fullest. He is known for being fun, cheeky, active etc.
This whole creation is a playground for God and if you are amongst the majority thinking Hindus, you will believe that we are one aspect of God living/acting on the stage that is this universe.
God has infinite attributes. He isn't just infinite in term of 'size' or vastness. He -is- everything. And this includes being playful.
Considering that Heaven is supposed to be a place of unspeakable joy and happiness, God almost has to be playful.
plus, look at all the cute and fluffy animals, heck even the creepiest and hairiest looking spider has a cuteness about it.
Even a vicious tiger is simply adorable.
All supposedly Gods creations.
Sorry if that's not the answer you were looking for