Is it possible to optimize a site, for a keyword that is not present inside it ? I mean.. I have a site that's maintained by another company, and I can't edit/change/suggest content to it.. This keyword I have in mind doesn't have much competition.. Is it possible?
Yes, it is possible. It is called google bombing but it's not so easy now. You just need to point a few links to the site with the keyword you want to optimize for as the anchor text
Google has done a very decent job at preventing google bombs from working. You should still get links to that site with the keyword in it - but you should also ask the people maintaining it to get that word in there somehow.
Tons of links are not required if it is a non competitive term. You'll maybe notice that your blog ranks for your name, even if your name is not on the blog because when you leave comments on other blogs, your name is your anchor text.