A MultiBit user has experimented with using a SOCKS5 proxy and it appears to work (I haven't tried it personally).
She started MultiBit using:

java -jar -Dhttp.proxyHost=127.0.0.1 -Dhttp.proxyPort=8123 multibit-exe.jar

i.e. localhost and her SOCKS5 proxy was on port 8123.

The Mac and Linux installers have the multibit-exe.jar in. On Windows the jar is wrapped into an exe file so you could not use it directly as you cannot pass command line options on. (You could grab the multibit-exe.jar from one of the other installers and it would work).

The current version of MultiBit will leak a little as the help is taken directly from http://multibit.org.
At some point I will bundle the help in the installer so this leak will disappear.