What about the back end of the tailpipe?
Does the outer pipe extend at least 3/8" past the end of the inner pipe?

If both pipes are even at the back (or worse, if the inner pipe extends past the outer pipe) the assembly will not create a venturi effect like it was intended, and as a result you will not have cool air being pulled between the two pipes.

I would not fly with the pipe you have. You will be nervous enough on the maiden flight without having to worry about your tailpipe collapsing on you, and if it does collapse in the air there is a very good chance that the back of your airplane will be nothing but ashes before it even has a chance to crash.

Wait for a replacement pipe, and don't fly until you are sure it is working properly.