It depends on whether or not "Manually manage music" is checked on the iPod. If so, you can drag and drop music from a second computer; otherwise it only allows syncing with one computer.
Yep. Or to put it another way since you used the word "sync", yes, you will lose everything on the iPod if you do a full sync with another computer. It will prompt you before it replaces everything though.
I do have the manage music option in place but after I drag and drop to the iPod and open the icon, the songs appear, but when I go to find and play them, they are not there.? Must be missing a step or something.