Google will notify you about error in Google webmasters tool, says Unreachable page or something like that ! If your server is down then it will show you the time/date and which page cant be crawled their.
Google has server response time as one of the characteristics to determine the rank of a site, so if your server is down, you will probably move down in rankings
Google doesn't do anything, If google doesn't reach to your page, It will show crawll error in webmasters account, and when your site is down for long time, then it'll negatively affect your seo.