How to check if a widget has no title

Nope, there is no way (thank I can think of) to do this cleanly.

Handling of output and related parameters is up to the each wdiget’s individual widget() method. There is no generic way to manipulate it.

You could maybe get away with filtering widget save or display instances to force it to always have title (like a single space string for example), but this would be meh semantically and likely visually.