Cheryl, besides the excellent points that Greg R is making, to answer your question, no. The iPod touch (any generation) can connect to the internet only through wi-fi. I am not sure if a jailbroken iPod touch can connect through bluetooth or the dock connector on the bottom. Drastic times require drastic steps :-) Hope this helps, good luck.
Have you investigated whether the 'Restrictions' feature in the iPod settings will meet your need? This might be a non-invasive way to accomplish what you want.
- Tap the 'Settings' icon
- Tap the 'General' menu heading
- Scroll to & tap the 'Restrictions' menu option
- Tap the 'Enable Restrictions' button
When you enable the restrictions on the iPod, the first thing you'll be asked to do is specify a four-digit passcode which will need to be re-entered the next time someone tries to access restrictions.
By default, most (maybe all?) of the internet-using applications are turned on. You can pick & choose which you'd like to turn off, as well as limit the ability to install new apps. There are a number of other settings which can be managed there as well. Restricting Safari, for example, will remove that icon from the display entirely.
If all you need to do is turn off Safari, FaceTime and YouTube, this is a pretty easy way to do it.
Hope this helps.