Is it possible to be a successful business and have a business model where you focus on website traffic with no ads, or immediate revenue streams, then after having good traffic introduce advertising opportunities
Absolutely yes. The truth is that the Web has about a 15 year history with proven business models. Mostly they work on volume. So if you have a huge audience, you can make a lot or at least decent revenue.
But if you have no audience, even the best business models won't make you money :(
Here is an example. Lets say you are serving ads in a good niche which gives you $10 CPM.
That means to make $10 you have to have 1,000 page views. So:
You see, you will make ten thousand dollars only if you get a million page views. Only a handful of sites get that per month. And that is considering a healthy CPM. So you see, without volume, things are tough.
Successful is such a loaded term isn't it? I will assume that you mean successful financially. We all know that there a lots of variables of success other than financial compensation.
Of course it is possible. Desirable, Feasible, those of course are all other issues.
What I wanted to highlight in your question is a great opportunity. If the long term goal is advertising or sponsorship revenue it would be wise to configure both your understanding of your business model and the resulting features/functions of the site around who the true customer and true product are. The customer will be the advertiser or sponsors. The product is the visitors and users of the site.
The more you know about about the site users, and the stronger affiliation they have with you - the more valuable they will be to your eventual customers later on. Developing systems from the get go that capture the type of psycho-graphic data that is "gold" to advertisers will make a different at some later point when traffic counts justify selling advertising opportunities.