I am a GoDaddy customer. I contacted Support, and the agent had not heard of Let’s Encrypt. He checked, and confirmed that GoDaddy does not support it.
I have formally requested support for Let’s Encrypt, but bearing in mind that GoDaddy is a Tier 1 supplier of SSL certificates, I find it unlikely indeed that GoDaddy will agree.
Still, one can hope, seeing as Let’s Encrypt will not invalidate its primary SSL business, as GoDaddy sells only expensive certificates; people after cheap ones (even GoDaddy customers) will purchase them elsewhere.