You could do that but that would not solve the problem, since the code that is in the try-block will not throw any other checked exceptions than IOException, and when it throws an unchecked exception you probably wouldn't want to catch it anyway. The code after the catch blocks would still be reached with in being null.
The != null check you showed is in the wrong place; it will actually make things worse there. You initialise the Stream inside a try; you use the != null check afterwards. If you have all the reading done inside the same try, you only need the != null check when you close the stream.