SEs request pages with the url and the ip address. As does everybody. Generally, when one requests a url with a browser, the request actually proceeds more like this:
1. You enter a on the browser address line, or you click on a url from another page.
2. Your browser uses dns to get the ip address for the domain extracted from the url you requested.
3. Your browser uses http to send the request through the web to url at that ip address.
Two requests are performed. First, DNS is requested to get the ip address for the url. Then, the page is requested from the internet with that ip address and url.
Usually, these requests are performed within a second of each other.
SEs do not, really, crawl by ip address. They use urls. It is only that Google, and some other spiders, for performance reasons, will do the dns lookup days before the page is actually requested. Essentially, google caches the dns translation information.
This technique may cause google and many other search engines to continue to request pages from an old ip address even after you have changed the authoratitive name server for the domain. This effect might cause some people to erroneously conclude that SE's "spider according to IP address" instead of according to the URL.
The worst case timing is like this.
1. You change the ip address in the name server for the domain.
2. The change propogates to the other name servers over a period of, typically, a couple of days.
3. If Google crawled at the worst possible time (just before your change was available to them through dns), they might still request at your old ip address after looking it up in their dns cache. I have seen the cache be as old as a week.
Which means that you should expect that some SEs might continue to request pages from the old ip address for 10 days after you change the ip address in you authoratitive name server. A month of overlap to run both servers while the change is being propogated is a good amount. Two weeks would probably be adequate.