Drive by download & execute vulnerabilities exist in Java for many browsers.
So yes, it is possible for the "trojan" to work as described.
So yes, it is possible for the "trojan" to work as described.
The applet has full access to the local filesystem with the same priviliges the original user has. If needed the hackers can further exploit the machine, by escalating user priviliges with some corrupt scripting..
One click is enough to seriously damage your machine, be careful;) This is what the popup looks like in Firefox http://www.ussu.ca/studentgroups/JavaApplet.jpg