Is there a loading delay without the splash screen?

If you have a blank or very light scene/project, and a paid license with the splash screen disabled, how long will it take to start up?

I was thinking of using Unity for a mobile app, but it would be important that it be responsive and open very quickly (or people would be less willing to use it, as you'd be opening, doing something brief, and repeating again later). Ideally it would be up basically instantly.

If it's still going to have loading time even with a simple project, I'd have to find another way (which I'd really rather not).

 

It will never be as fast as a small native app but the loading time mostly depends on the first scene you are loading.
A small menu or a custome loading scene does not take long to load. And not i cant give you a fixed second answer because A: its Content depended and hardware dependent.