Yes, I believe so... basically all the plugin does ( I think ) is tell the browser, "When you run into a Java program ( defined in an object tag, so the browser will run it with a plugin ), use this program ( the Sun JRE ) to run it instead of this one ( the browser JVM )." I think that the JRE that actually runs the Java program is the same on that is distributed as the JRE.
Write once, run anywhere, because there's nowhere to hide! - /. A.C.