Ok I have 2 computers with 5 miners (cards). I use Deepbit and GUI miner (used to use POCLBM but switched recently). For the last while I have been running only one computer which has 2 miners. My question to you is: does the mining software take a lot of bandwidth? I can't imagine it being more bandwidth than downloading a torrent.
Only while trying to download the blockchain, like any other client. Ongoing, not so much, no.
Also, will porting through the TOR network really hide the packets from my ISP?
If set up correctly, yes.