When I stopped doing all my own customer service at CD Baby, I found someone even more patient, playful, and charming than me. It sets a high bar, so that if you grow to needing an entire team of customer service people - (I had 28 full-time customer service people in the end) - then you and your first one or two really set the expectations for how caring, helpful, and charming they should be.
Definitely don't just outsource to a cheap provider or cheap person. Whoever is actively communicating with your customers should be the best of the best.
I wrote a small piece on What Your Startup can Gain by Delivering Great Customer Service: http://www.happyfox.com/blog/what-your-startup-can-gain-by-d...
As a passionate founder, you would have the right tools and people that will keep you customer service going.
+1 for founders to be part of customer service irrespective of the size of business.
However, I'd argue it is generally not applicable. Say you launch a free application (perhaps monetized by a supporting PRO version, in-app purchases, or ads) that gets a few thousand downloads per day. As a CEO, you can't spend your precious time replying to those (99% trivial) questions.
You may do it for a few months, or a percentage of the user questions, to gain insight into your customers. But, as a rule, I'd rather outsource it.