No!  You need an air compressor.  Blow, with the air chuck, into one outlet while plugging the other outlet, and air should come out of the inlet.  You should hear it.  Don't put your hand under the inlet to feel the air!  When the chunk lets go, it could inject it into your hand!  I don't follow your front and back as I don't know what cooler you're using.  A newer Raven cooler has a 3/8" FPT inlet and 2 - 1/2" FPT outlets.  Blow into one 1/2, plug the other 1/2, and air will come out of the 3/8, eventually.