Definitely not my go-to first response, but I've been known to tell my SO to google whatever question he has on occasion. Those occasions being when we're driving home after work and I'm plugging away on my phone at something I've wanted to get done all day, but couldn't because of work, and he decides he needs to ask many questions in succession. I will try to answer them as much as I can, but it does sometimes land on "I don't know, you should probably google that". Which usually gets a me "Okay, you're not driving, you google it." Which... yes, I could, in fact google it to give him the satisfaction of the answer right then and there, but I am also very obviously doing something and the thing that I am doing is not less important than some random piece of information you decided you needed to know thirty seconds ago.

So, like many have said, definitely not a go-to response in general conversation, but plausible in some situations.