That was always my intention. It's not a hard and fast distinction, but I generally play the "tournament" fights or the "major plot point" fights with the full system, and all other fights with Dramatic. The only difficulty I sometimes have with that is that some players prefer the speed and narrative elements of Dramatic over the much gamier full system, and thus feel a disconnect in the fight scenes that are supposed to be the most important.But when I get some time, I'm considering running a pbp Dramatic-only game to see how it feels.I too would love to hear others' answers to Kim's question.
To answer your new question, absolutely yes - but I don't think there are any special chargen 'traps' involved. Combo machines lose one of their greatest tactics in Dramatic Combat. Characters that max out non-combat skills have more options in Dramatic. Characters with lower Level Special Moves can use them in Dramatic a little more often.
I think the Director needs to keep this in mind when looking over characters, especially if a character is hyper-focused for one system but very weak in the other. Otherwise, if the two systems are being used pretty equally, I'd let the differences between characters stand.However, since this might require a certain amount of system knowledge, I'd be inclined to let players shift things around once play began to better suit their vision of their own character.