I would say it is possible, but not guaranteed. Numerous factors beyond your control will impact how quickly you can get your site listed - how soon Google is able to actually crawl the content (depends on how many things have been pinged in), how quickly your DNS entry is able to propogate, and how Google evaluates your content once they access it, among other things.

A new domain should be accessible within an hour in many cases (again, no guarantees, but on average) and once Google is pinged, the content is often indexed within an hour (sometimes as quickly as minutes - but again, no guarantees).

__________________
The best way to learn anything, is to question everything.