Converting to Threadless

[jf21557]

I have an old road bike with a 1" threaded fork with a broken dropout. Nashbar had a sale and I picked up a replacement threaded fork. What I failed to realize is that the threads are only on the top couple inches or so of the steerer. I ordered this fork with a fairly long steerer and it is obvious that when it is cut to length, there will not be any threaded tube left.
The bike has the original headset and I was going to replace that. I have a threadless stem (1 inch) tucked away somewhere, so I could go either way.
So if I obtained a 1" threadless headset, plus my 1" threadless stem, and with the fork cut to the proper length (thus making it now a threadless fork!), any reason that shouldn't work?

Thanks folks.