Short answer: no, your Google Apps admin can NOT see your web search or YouTube history.
I'm a Super-Admin (highest level) for my company under Apps for Business, and I can't find any YouTube or web history activity via my Admin console.
What I can do is see a log of email going in and out, and enable or disable Chrome history syncing for my users (but can't see the contents of the history).
If you have a corporate VPN or something like that which you were connected to at the time of your NSFW browsing, you might have been accessing the Internet via your company's network, which they could certainly inspect, but other than that I'd say you're in the clear.
(Note also that if your device was supplied by your company, and not personally owned, you can't guarantee it doesn't have software on it which reports usage back).
I also found this Google Apps forum thread, confirming that admins can't access your history: http://productforums.google.com/d/topic/apps/oS1_LnvfzX0