I thought so too. Your question has nothing to do with the finally block. Finalization can happen on objects that do not have any try/catch/finally blocks at all.
This is what the API states of finalize method
The Java programming language does not guarantee which thread will invoke the finalize method for any given object. It is guaranteed, however, that the thread that invokes finalize will not be holding any user-visible synchronization locks when finalize is invoked. If an uncaught exception is thrown by the finalize method, the exception is ignored and finalization of that object terminates.
After the finalize method has been invoked for an object, no further action is taken until the Java virtual machine has again determined that there is no longer any means by which this object can be accessed by any thread that has not yet died, including possible actions by other objects or classes which are ready to be finalized, at which point the object may be discarded.
I believe this means,that even if an exception occurs in the finalize method, the object still remains eligible for garbage collection and it will be garbage collected eventually.
HTH