I was in batch[1] and worked on the back end of a startup simultaneously, but not while on HS time. Having had the experience, I wouldn't recommend HS if you're more interested in startups than you are in programming. The goals are completely different. The measure of a startup's success can be directly observed, but you can't simply observe an overwhelming sense of curiosity or the triumphal sense of discovery. The reason I'm interested in startups is that it's a way to spend all of your time creating things that enrich other people's lives, which is exactly what we try to do at HS.
Then you have the concept of ownership and monetary gain, but nobody really owns HS projects, they just happen. There are no contracts or points, there is only the joy of programming. When you naturally put people together that are all working to better themselves in the same way, they wind up cooperating. It's much easier to cooperate on something that's already shared.
Now that's not to say that you can't do anything tangentially related to your startup while you are working on HS. I wrote and open-sourced a library that was tangentially related to my startup, but I did it as a learning experience; it wasn't mission-critical, it just scratched an itch. I wound up not using the project on my startup because it contacted an API that changed, which crushed my curiosity and caused me to stop working on it, but looming in the back of my head, it gave me some inspiration for the curiosity that HS satisfies.
In hindsight, I wish I had never written that library. Yes I learned from it, but my time would probably have been better spent reading Erlang and OTP in Action.