That likely won't work -- I believe the Java web plugin is blocked for ALL browsers, though I haven't tested it.
Because of the severity of the security problem (sigh -- AGAIN) in Java, there's not much you can do until Oracle deigns to release yet another patch, which presumably they are working on ...
I'm happy that I don't have ANY Java dependencies in either my regular sites or programs that I'm aware of. I keep Java up-to-date just in case its ever needed, but so far it's stayed disabled from one of the previous times it was deemed dangerous to use it (which has happened A LOT over the last few years).
As for people who need for stuff like LogMeIn, you may want to start looking for an alternative program that doesn't rely on Java -- or get used to "outages" like this, cuz this won't be the last ...