My wallet.dat's filesize was 70 KB.
I encrypted it with bitcoin-qt.
Then it was 53 KB.
It rebuilds the file which compacts it by removing housekeeping space that BDB kept around. It should almost always be smaller.
Assuming I have a very secure password, it's safe for me to widely distribute my new, encrypted wallet.dat, right?
I wouldn't advise it. You'll reduce your security from two factor to one factor... and the encryption doesn't protect your privacy it only prevents spending/signing. Also, the wallet will eventually go out of sync once you've used up the keypool.