This automated approach is fine, but only if you don't try to pretend it's personal. SlideRocket does this really well - sign up for SlideRocket and watch the helpful emails roll in. Not too many, and always with a good tone and good content. But none of them pretend to be produced by hand in Gmail.
Sending personal emails to the first 1,000 customers is great, and switching to automated lead nurturing after that is great. Partly for scale - there are a hundred high-value things a CEO can do once a business gets going. But also because customers don't think it's appropriate to get a personal email once you grow to a certain size.
Anecdote: I've been heavily involved in our sales process at Zencoder since the beginning (as CEO), including writing personal emails to 500-1000 signups early on. (We've stopped that by now, but it was the right thing to do early on.) A few months ago, our sales director and I went to meet with a high-value prospect. At that point, their financial value wasn't huge (hundreds per month), but we knew they would grow, and that they'd be a good reference customer. So we pitched them and everything went well.
I ended up meeting with them a second time, and they asked me point-blank: "How is your business viable, if we're only paying you $X00/month?"
The subtext was this: "If we're only paying you $X00/month, and we get the CEO in for two in-person meetings, then you must be small, and we must be a critical customer for you to win." Customers should feel important, but never critical.
This came to a head when we sent them a final proposal. They asked for a price break and concessions, and said explicitly that because they were an important customer for us, we'd give them these things concessions. In reality, they were no more important than 20 other prospects we were working with. But because we brought our CEO into sales meetings on a small deal, they thought we were smaller than we were.