Alternator question

On my 71 demon I replaced the stock alternator with a chrome Tuff Stuff one with the built on regulator. I removed the external regulator and the wiring installed the new alternator. I did not run a wire from the alternator to the positive battery post. Instead I used the stock connection from the alternator. Will this work? Or do I need to run a wire from the alternator to the battery for it to change?
Thanks for any input