Why would you want to place advertising on your cool site just to submit your site to google? You can put <meta> tags on your webpage to add your site to google/search company, like the following:

well, you are certainly right that we can use the meta tags for the inclusion of the site. however things change and so have search engines. Earlier meta tags were enough for the search engine optimization but they were used to bring false results as anyone can use anykind of KEYWORD...however now the search engine wants to make sure that the search results must be completely accurate and for that they use different technology and different ways to index and include the site.

It is not neccessary to include the ads however including the adsense will make sure that your site will be scanned by the Google Bots and thus it get the chance of getting scanned much faster.

Although it is not required to have the adsense for search engine to crawl your site...!

Yes, I can say by my own experience that if you place adsense advertising on your new page, it will be indexed much faster. With adsense takes to be indexed less than a week. It's nothing bad!

From my personal experience, I tell this does not work. Google did not crawl my site for indexing even after putting their ADs for more than a month.(May be they have modified the practice now). Better go and submit your site formally.
And one more thing, most smaller search engines are linked with Yahoo Search. So it's a better idea to keep Yahoo also in mind.