Googlebot would have to be indexing your site at the very moment that it was down for anything to happen and even if it's down for a half a day, from my experience, rankings are unaffected.
However, there's a small side-effect. If visitors that are coming from X, Y or Z engine, visit your site and there is a 404 or Server Error and they click the back button or get the "Google Can't Find This" page, it can, for that period of time increase your bounce rate. If the originating click starts at say Google and then the clicker goes back to google, it tells google that the page wasn't what they were looking for in relation to the term that they used, or that it didn't load, or that there is a problem with it. Basically any reason that can be tied to bounce rate.
As alarming as that may sound, I don't believe that it would effect your rankings.
The easiest way to see if Google noticed is to log in to your Google Webmaster Tools account and check for errors. If they list any errors such as 404 or "server unavailable" (which I'm not sure they have that one) for any pages that you know are usually live and well, then you'll know they noticed.
But again, I'm not under the belief that it will largely effect your rankings. I've read from Google's words that they do go back to sites that were unavailable or down and try to continue their index.
As for your server being down for 12 hours. That's a lengthy amount of time. I can't even imagine it. You might want to check your hosting capabilities. You should be back up and running in minutes, not hours.
Just to give you a some piece of mind. I have a plethora of affiliate sites that make a small income for me. I once registered a domain name that a very large corporation didn't appreciate. It had a trademarked word in the domain. Long story short, my domain info was set to private so they got legally got the server shut down. I didn't know for days because everything was on auto-pilot and I wasn't checking my related email addresses. When that server was shut down, 100+ websites on that server went down too because that one trademarked (partially) domain was on the same server and same hosting package. The sites were down for about 5 or 6 days while I sorted through the legal paperwork. After I made an agreement to give the big company the domain, minus the 20K in damages that they originally wanted, the hosting company turned the server and hosting package back on.
Not a single one of the domains lost ranking. Not even 1 spot! Today, they still rank in the top 2 to 3 of their biggest terms. So my words are truly from experience and are from a worst-case scenario. I think you'll be fine.
Finally, to clear the air. I didn't do anything bad, nor would I ever do anything bad with a domain name (other than keep it in my portfolio). The big company was upset that I got the domain before they did. All I had on the index page was their description of their product that was named in the domain. That was enough to be taken down for copyright and trademark infringement.
In the end, that company was actually very cool about it. And it's a Fortune 10 company! I was surprised!
