Yes, you can create a zipped up JDK, unzip it on the target machine and run java, javac, etc. from that directory to your heart's content.
The easiest way to create such a zip file is to install the JDK on a machine and then zip up the contents of the JDK directory. We do this in certain circumstances where we need to control exactly what configuration of Java will be used in our deployments. In that case, our scripts just point JAVA_HOME (or the equivalent) to our internally bundled JDK instead of relying on a sysadmin to install exactly what we need prior to arrival.
In terms of integrating with the browsers, that can be a bit more problematic. The short answer is no, you can't integrate directly with the browser without some sort of installer.