If I have iTunes Match and an iPod Touch 4th Generation, once I upload CDs to my iTunes, can I delete the songs from my computer without deleting them from the cloud and my iPod?

I am a K-5 music educator. I have classes back to back all day and sometimes need to take my music to different rooms/buildings/cities. Instead of carrying around the literally hundreds of CDs I need, I got an iPod. Unfortunately, our district only has about 10,000mb of space for each teacher to save to on our individual drives on the computers, so therefore, I can't upload all of my music into iTunes from those CDs which also means I also can't get it onto my iPod. I'm wondering: if I get iTunes Match and an iPod Touch 4th Generation, once my stuff is uploaded into the cloud (with Match it does upload CDs into the cloud too, right?) can I delete it off the computer? Right now, I can't even save a little tiny word document on my computer let alone finish uploading the rest of my music!!!