Abosolutely! I built my own site completely via word of mouth, and it's now in the top 5000 US websites on the internet.
Building a business via word of mouth takes a LOT of time -- you'll need to dive in and really be a contributing member to the online communities that are relevant to your niche. Most communities aren't very tolerant of blatant advertising or self-promotion. You'll have to really add value, get to know other individuals, and be willing to put a lot of time into it.
Ironically, even though I built my own site this way, if I could go back and do it again differently, I would have definitely found a way to put $10-$15K into a marketing budget for advertising and a professional publicist. Just because you CAN build a site on the cheap with word of mouth, doesn't mean it's the best way to do so. My business would be a lot farther along now if I had put more effort into finding the right capital to cover promotional costs.
At the same time, word of mouth marketing has a wonderful side effect -- free market research. As people spread the word about your company, they will be quite honest about what they like and don't like. It would make sense to at least wait 6 months or so until you put any money towards marketing until you have a site that you know people will really love, based on the feedback they will freely give you along the way.
Lastly, when you do start your word of mouth marketing efforts, here are the areas you'll want to be sure you have covered:
- Social Networking, such as:
- A Blog - a MUST
- Social Bookmarking
- It takes a little while to learn what works and what flops with social bookmarking sites, but Digg, Reddit, Propeller, StumbleUpon & del.icio.us are big traffic drivers
- Here's a primer article I wrote on my own blog to help you get started:
An Introduction to Social Media Strategy and Socially Driven Content