No, it's not ok, now eat your supper and go to bed!

Presumably you're a grown adult, you don't need our permission to do anything. You're asking the wrong questions.

You should be asking, what is it I want to do? Will 3 weeks be enough? (it won't) Does my employment contract allow for this? How would they even know unless you tell them?

Work on it in your free time, don't tell anybody, especially your employer. When/if you're ready to launch and if there's going to be a conflict of interest you can quit then.