Restoring an iPod on a Windows computer will erase all the songs and data. Essentially it sets it back to factory defaults. Restoring on Windows will also format the iPod hard drive to a Windows format, which is Fat32. A mac restore will set it to HFS. As a mac can read Fat32, you can plug an itouch that was formatted into Windows and it will work, but not the other way around.
As for the rest, the iPod will only sync with its original library, so if you plug it into a computer to charge it will not sync automatically. It will though pop up a message stating that your iPod is currently synced with another library and if you would like to sync with the new one on the new computer. If you say yes, then it will erase all the data on the ipod and make the new computer its home computer. You can, though, transfer purchases without erasing your content, but unless the new computer is authorized on your account they wont be able to use them.
So, yes you should be able to plug your ipod touch into any computer without any fear as long as you do not specify yes to sync to the new library.