It seems in the AMA they mention this was something that basically one other interaction could cause to occur. As far as I can surmise from my own understanding of the rules, if the permanent has no type and isn't a creature you can't attack with it. You also clearly couldn't mutate it further. Could be a nice trick to make it hard to remove on other people's turns if you had a way to reliably turn it on during your turn and off during opponents, otherwise seems like something to not do.Q: What happens if my mutated pile contains a Theros God but I don't have enough devotion to make it a creature?
A: It'll stop being a creature. If the God isn't at the top of the pile, you will have a permanent without a type.
Seems like a pretty harsh non-bo and a good reason to not mutate a god into a pile anywhere. Then again with a deck like this the number of distinct permanent contribution to devotion is probably lower than average and they're rarely turn on to start.