Java: Exception thrown in constructor, can my object still be created?

No. Look at the client code:

Test myObj = null;
try {
 myObj = new Test();
} catch(MyException e) {
  System.out.println("" + myObj);
}

Here, when exception occurs, the '=' operation is not executed. Your code goes straight to the catch block and myObj stays null.

A class instance creation expression always creates a new object if the evaluation of its qualifier and arguments complete normally, and if there is space enough to create the object. It doesn't matter if the constructor throws an exception; an object is still created. The class instance creation expression does not complete normally in this case, though, as it propagates the exception.

However, you can still obtain a reference to the new object. Consider the following:

public class C {
    static C obj; // stores a "partially constructed" object
    C() {
        C.obj = this;
        throw new RuntimeException();
    }
    public static void main(String[] args) {
        C obj;
        try {
            obj = new C();
        } catch (RuntimeException e) {
            /* ignore */
        }
        System.out.println(C.obj);
    }
}

Here, a reference to the new object is stored elsewhere before the exception is thrown. If you run this program, you will see that the object is indeed not null, though its constructor did not complete normally.