of course you can. but i think you need to do good SEO before that. If your site has good keywords and high alexa rank, people can easily find it on google. To me, i always check traffic of my website before place Adsense. Siterank.me can give you correct information about your website visitors and others information. If your site has large number of visitors i think you should place Ads on it
In reading through your responses here it appears as if you just want any old website to make money from. In all fairness you're probably better off looking for a part-time job or perhaps changing careers because what you ask isn't likely to happen. First off, if you have a Website that you're simply trying to milk for advertising revenue, chances are you're not truly passionate about the site. This will reflect in your content which will make it impossible to retain, let alone attract, traffic. This even assumes you index well which you're probably not going to because of Google's wealth of metrics that clearly determine how visitors value your site. If you want a chance of making money from your site then create one with a topic you're passionate about. You will enjoy filling it with content and will likely offer up information others have not leading to better chances of indexing well. Any site in any niche can do this providing it's full of unique, informative (or even creative), well published copy. Even this may take time, perhaps several years before you even start to see a few hundred dollars annually. ...thinking this will happen on a new site is completely unrealistic, sorry. If it were that easy everyone would be doing it.
Honestly, it's about the traffic. The more traffic you have, the more likely you will see $1,000 per month.....this is the bottom line, everything else people are mentioning are just semantics.