I think this works if you're a one man shop...once you hire employees, though, things change. A lot. You have to keep your business running because your devs have trusted you with their family's financial well-being; you have a responsibility to keep the business healthy.
How much "keeping things running" is actually needed? I'd imagine disappearing completely for a couple months wouldn't work, but what about a couple months of signing on only on Monday mornings?
I think that's contingent on your business model and the maturity of your company.
I can only speak to my biz: most of our revenue is service (although we're trying to migrate to product). So we have three primary "departments," if you will: sales, production, service/support. I've chosen to staff out "production" first with kickass developers. But somebody has to take care of sales and service. Service/support, we've automated that pretty efficiently and only bother devs with processed support issues.
Sales, however, still requires the cultivation and management of client relationships. You can't just phone that in, and the way we've grown our business has been via relationship (i.e., referrals and word-of-mouth). So even if I was 100% out of production (which I'm not, yet), there's still the bizdev side.
At least that's how it is now; two years in the future I'll probably have a different answer and perspective. A lot of this stuff you just figure it out as you go; there's not a book out there that tell you how to run your biz.
