Your first question is really two questions:
1. Can you successfully grow a company that you start part-time?
2. Can you successfully grow a company while you're still part time?
The answer to the first appears to be yes: among others, this describes Microsoft, Apple, Amazon, EBay, Facebook, PlentyOfFish, Bloglines, and Del.icio.us. It almost seems like companies that do this tend to do better than the ons that jump in all the way immediately. The extra time gives you a chance to do the riskiest parts of your startup - market research and prototyping - while still under your employer's umbrella, and it's a test of your commitment. If you're passionate enough to put 4 hrs/day into your startup while still employed, you'll be in much better shape when you're not employed.
The answer to the second question appears to be no: of the list above, EBay is the only one that made enough money to support the founder at his previous salary before he quit his day job. There's just too much that needs to get done at a startup to do it all in your free time.
As for my own story - I spent 9 months working part-time on my startup before going full-time. The immediate effects seem to be that it set us back 9 months, and I have about $30k more startup capital. There're likely 2nd-order effects as well; for example, because of the 9 month delay, my cofounder got accepted to HBS before we launched and quit. OTOH, if this recession turns out to be long and deep, the delay and extra capital may mean the difference between falling down dead in the middle and making it through to the other side. And in the 9 months extra I spent at my job, I got to see my project go from "death march" to "almost done", which is good practice for when your startup starts looking an awful lot like your last employer's product.
I also shared your fear about becoming too busy and worn out from the job to pursue my entrepreneurial dreams, but this fear turned out to be overblown. You don't magically become a different person when you take a corporate job. If your startup is compelling enough to sustain you through the inevitable low points, it'll be your job that suffers (and then you just need to realize that and back out before you get fired).