Yes, you need an internet connection to jail break. However, I am not sure if you can jail break using the 3G connection. And, a quick Google search didn't help me find the answer. So, hopefully, someone will come along who can answer that part for you. Sorry.
One thing I can, and DO, recommend, however, is that you go ahead and upgrade that iPad2 to iOS 5.1.1. Yes, the iOS you have can be jail broken with the original Absinthe, but the newest Absinthe (version 2.0.4) can jail break the newest iOS. Just makes you as current as possible...
And, before you upgrade, do make sure you have a current/fresh backup. Then, after you put iOS 5.1.1 on the iPad, follow the prompts from iTunes to restore as new (do NOT put the backup on the iPad at this time). Then, jail break with Absinthe. Once the jail break is complete, THEN you can "restore from backup." iTunes will then put all your apps and settings back on the iPad. Once the process is complete, your iPad will be as before, except with a fully up-to-date iOS and jail broken.
And yes, if you don't like the jail break or it doesn't work, you can do a restore and iTunes will put your backup onto the iPad with the apps being in their installed state - they'll be transferred from iTunes. Just a warning though (and another plug for iOS 5.1.1) - if you have to restore that iPad, you will have to go to iOS 5.1.1, which is the current, Apple-approved iOS.
Hope some of this helps. Good luck and do let us know how you get on.
Marilyn
P.S. And, since you talk about a jail broken iPad, I've taken the liberty of moving your post over to the Hacking section. Thanks for your understanding.
