I would not recommend trying to do this.
1.) It doesn't anonymize you any more than you already are (bitcoin is already anonymous and decentralized)
2.) Bitcoin client is essentially a torrent client. You are not supposed to run this on tor--it harms anonymity and puts undue stress on the network.
3.) Using tor browsing is safe enough--your goings on will not be tracked. If you're worried about it, use something like instawallet.
1.) A connected node could potentially identify the ip address that broadcast the transaction.
2.) Much lower bandwidth than a torrent... really not that much traffic.
3.) Instawallet is a good suggestion. If you want to run a native client on tor anyway, and you aren't on Windows, torify is your friend. If you run Windows, ask someone else.
+1, except don't ever store your bitcoins with anyone unless your situation absolutely requires it. The rise of bitcoin "banks" and similar such is not a good thing.
Also, I wouldn't worry about the bandwidth requirement for the blockchain unless you are on an analog phone line or a 3G wireless connection, nor the data volume with respect to Tor. I did find that going through Tor resulted in fewer bitcoin peer connections and seem to greatly increase the latency of transaction confirmations.
Anyway, bitcoin isn't anonymous. To the contrary, it appears to me that it could be a good platform to train people in the principles of detecting activities that may be money laundering or other no-nos. Nice to have that blockchain out there, one wouldn't even need to generate a student example database.