Cool, is this your site?
No. I'd be bragging if it was. : )
a long random string of numbers and letters
Generating random keypairs and using the public key in the URL and the private key for the password would be plenty strong.
If two or more people had a pre-agreed string for hashing and double hashing data using brainwallet.org, a fairly secure method of communication could be developed from something like this.
Example (not a good one necessarily, but enough to get the idea across):
Our pre-agreed string to generate keys is using the name of the day + gold's high price in dollars fom kitco.com (no pennies) from the previous day + an _. In this case, we'd end up with the string Monday1271_. If I want to send you a message, I go to my offline version of brainwallet.org and put Monday1271_ as the passphrase. The resulting public key from this operation is entered as the new brainwallet passphrase and the public key from the second round of hashing is our URL:
http://www.protectedtext.com/14SKwefGgQ31aqtdSRThQN1cTwoKxEWhVuThe password is the private key which the receiver can generate using the same process used by the sender using the agreed upon scheme. I even left a message there if anyone wants to try it.