yes, but a question mark at the end by itself is different if it is used to call a stored function on their server.
btw, I don’t use no-ip. But testing the urls is still possible. Because finding out if the outside ip has changed is a simple public record lookup that can be done anywhere.
The url with the ? calls the public record lookup while without it does not.
I give you information. its up to you if it makes sense to apply it. Quite frankly if you have to waste money on a service like that, I would get a different isp so I would get a real public ip and if it was just a dumb web server, its way cheaper to host online. I charge $60 /year for such trivial sites.