If I understand, what you're suggesting is like children's sweaters that have an extra band across one shoulder. Usually you just continue the stocking stitch of the sweater body as k2p2 rib when you get to the shoulder. On the front the band has buttonholes and on the back, it's a buttonband. You can certainly do this but you may be happier after all the work on the sweater body, if you take out the neckband and pick up sts with a larger size needle. This will help especially if you think it was in the initial pick up that the neck became too tight.
Well, give one of the methods a try and see if you like it. The good part is that you can always take it out the re-do it.