Yes and no. You might be connected to WiFi, have no Internet and still not be an ISP issue, if you are using a third party DNS that fails. Or if your router is under heavy load and can't process all packets. Or if there is excessive interference in the specific Wi-Fi band in use.
That's to say there's no definitive answer to anything, without investigating the root cause.
But really, the majority's of problems seem to lie on the client side


