What are you using Fireworks to do? Remember its intended role isn't photo processing - it's for creating web graphics like buttons or complex rollovers with associated scripts and HTML. If you are slicing up a photo to use it in such ways, there might be a point to using it, but not if you're using it as an alternative to Save for Web.
Yes, save the profile. At least then there's a chance that others with colour managed systems and using colour managed browsers will see pictures approximately like you see them. But don't forget that even if you do save the profile there are visitors with non-colour managed systems and non colour managed browsers, and it's pot luck whether they'll get similar colour to what you'd expect.
John