That really has more to do with search engine optimization , content of your site, and external links to your site than where you host your site.
You may find This Article interesting .
It varies depending upon factors, such as when the sitemap was submitted to Google and how busy Google is. Content type may also play a role but typically you should appear somewhere in the results within 48hrs of the sitemap being scanned (see google webmaster tools) wherever the domain is hosted, however it can take as long as thirty days in some cases. Where the site will appear in the rankings at first depends largely on the CONTENT and how UNIQUE or RELEVENT it is.
To pre empt your next question..
GoogleBot re-scans sites without adsense content on a weekly basis at first then dropping to monthly (even yearly) if no new content has been discovered. On the flipside where new content has been discovered the freaquency of scans can increase to daily. Figures are only a rough guide but you get the idea hopefully.
Google is the undisputed king of Spartan searching. Google is fast, relevant, and the largest single catalogue of Web pages available today. Make sure you try the Google images, maps and news features. They are outstanding services for locating photos, geographic directions, and news headlines.
Do Off page optimization works then you can get the backlinks for your website. Off page optimization works such as directory submission, link exchange, article submission, social bookmarking.
Basically Google takes time to index a website. You have to put your link in google webmaster tool manually. you have to do some social bookmarking with high PR dofollow bookmarking site.
In general, webmasters can improve the rank of their sites by increasing the number of high-quality sites that link to their pages. For more information about improving your site's visibility in the Google search results,I recommend reviewing Webmaster Guidelines.