I have a sitemap link in the main page of my site but I dont want to submit it. Will Googlebot crawt my site if I dont submit a sitemap?
Yes they will. For them to exclude it just exclude it in robots.txt All bots won't respect that but Googlebot will.
You can also submit it from the robots.txt , google ,yahoo,msn made standarts for it. You can add Sitemap: <sitemap_location> in your robots.txt
you can add it your robots.txt file. sitemap:your-sitemap-file-url and one more question; why dont you want to submit your sitemap to google webmaster tools?
The frequency and depth of your Google-crawls depends on many factors such as age of the site, number of incoming links, PR, phase of the moon, and the mood of the GoogleBot. Basically, if your site is new, it wont get crawled very often..
I suspect that the OP is talking about his .html sitemap when he speaks of having a link to it from his home page. I can't think of any reason not to allow Google to crawl that. And of course he should submit an .xml sitemap to Google Webmaster Tools (and also to Yahoo! Site Explorer).