In fact, why not take it a step further and make a stand-alone client that only executes the byte code? It would be different from Java for two reasons:
(a) The bytecode format could be much simpler if it weren't tied to a particular language (no type system, no objects, maybe not even a garbage collector). If the bytecode was similar to a real CPU architecture, it would be possible to target it from LLVM.
(b) There would be no humongous standard library to install, because it could just be downloaded on demand. With almost all of the library living on the server side, application authors could avoid a lot of the usual compatibility nightmares with different client implementations each one with its own bugs and workarounds.