Would you hire a programmer who would view their work as their startup?

Can you clarify a bit? Are you saying that the hire in question aims to view whatever work you assign to them as conceptually "their startup" and they will bring startup energy to your project? Alternatively, are you saying that you will assign them work and that some time in the future they intend to take the ideas/concepts they learn and create a (rival?) startup out of them?

Many projects fail and when it happens the first time, many participants feel gutted. One of my first assignments out of college was to work on a large project and literally on the eve prior to going to production, the company canceled the project as advances in hardware had made the product obsolete. I was devastated, but one has to learn how to pick themselves up and move on. After all, they paid me to build something and I did. It was always out of my control to determine what they did with my team's work.

I wouldn't hire a programmer unless it was perfectly clear that I (or my employer) owned their work. They couldn't go off and use the code in their own startup situation.

Is that the scenario you're talking about?

If “start up” means getting off their perverbial ass and conquering the challenges of others then yes.

Take it for whatever it is, if it is effective and provides you comparable value.