Yes and no, (but mostly no! :)
No, it's not possible (the most sensible answer):
For every call, there will be an activation record pushed onto the JVM call stack. This takes a non-zero amount of memory, thus you will at some point run out of memory, at which point a StackOverflowException will be thrown.
Yes, it is possible (the super-theoretical answer):
There is nothing in the Java Language Specification that explicitly says that you should eventually run into a StackOverflowException. This means that if you find a cleaver enough compiler, it may be intelligent enough to compile this into a loop.
A related question would be, "Does the JVM support tail-call optimization." The answer to this question is, "no, not at moment, but it's not ruled out for future versions".