Absolutely fueled the fire. Don't consider it rejection as much as "non-selection" as someone else said. It doesn't mean you have a bad idea or aren't good at what you do. There are just so many spots. If you believe in what you have, you find a way to make it work.
Hard to see how it could be a good thing. The added desire te succeed, if any, will likely be short term.
The fact that it might be a good thing is personal (aside from the added desire, which could very well be the final straw to motivate whomever to do whatever). I was a bit nervous about quitting my job - that decision has been made for me.