John Mueller from Google released another #AskGoogleWebmasters video where he said the only real thing that changes, temporarily, when you move a site from one server to another server, is how fast GoogleBot crawls that content. Google will throttle back, in order to test to see how fast it can crawl your site without impacting your server in a negative way.
Here is the video:
In short, assuming nothing else changes with the server move. The only change will be that Google slows its crawl to begin testing how fast it can crawl your site within taking the server down because of overloading it. Outside of that, you should be fine.
John also mentions the server migration help doc it published a while back to help guide you through these changes.
Forum discussion at Twitter.
