Back when I was 20, I did a job like that.
Rest assured that your net techs can check your logs, but they DON'T usually care enough to do it, unless they have reason to. Like your manager asking them for a report. Or sheer boredom.
However, you trying to break their firewalls gives them a reason....and who knows? They might get ticked and send a little email to your boss with a log of what you were up to. If you think your boss wouldn't like that.....then you should probably stop trying to beat your techs.
Instead, make a friendly phone call, or WALK to their desk and ask them for help getting to this site. They may solve this problem for you, or at least get you a definitive answer like: "We blocked this particular port because people spend too much time on Bulletin boards during the day" or something.
That would give you a major hint to do your browsing at home, because they're watching YOU.