No, pretty much not(the blowing out part).
JDBC is pretty threadsafe.
But once you create Statements and execute them, they shouldn't be mutated concurrently.
(The only thing you maybe could do (YMMV) is collect the results in parallel).
But I am very certain that once a Driver must go to the backing store to fetch data, there probably isn't much the Driver can do in terms of threadsafety.