I tried to do this in December, and would have succeeded, however, my niece got sick and we had to leave DL. We watched the parade at DCA near the front of the park. Immediately after it finished we made a beeline for DL. We got onto Main Street about 5 minutes before the fireworks were to start. We were near the back of Main Street as it was very crowded, but we didn't want to push past those who had already been waiting. The view wouldn't have been great, but we would certainly have been able to see them. About a minute before they were going to start my niece told me she was going to be sick so we left. I think this may be harder to do during the busy season as the lines to get out of DCA and in to DL get quite long.
You actually can see the fireworks from Downtown Disney as well so you don't really need to go into DL if the line is long.