Are we talking about the same kind of promotion?
When you ask about promoting the site, I assume you mean that you will look for other sites that have a similar audience, make contact with the operators (in a non-spammy way), and make sure they know about your site. You might engage with like-minded people in forums, and you might get yourself known in the relevant blogging community. All of those actions will enhance the reputation of your site, and will eventually lead to high-quality links.
If that's what you mean when you ask about promotion, I would say that you should start doing that right away, that you should do as much of it is you can, and that it will do no harm whatever to your rankings.
But if you take promotion to mean submitting links to directories, engaging in link-swapping schemes, spamming forums and blog comments with links, and similar dubious practices, then the answer is that that can indeed hurth your rankings - and it won't give be you any benefit at all, no matter how quickly or slowly you do it.
I assume you weren't planning to take that second approach, but I thought it worth clarifying that point.