I think it depends on your situation. If you get self-conscious and all worried and stuff, then no. But if you're aware of your own limitations and you're aware that most things can't be fixed in a few minutes, then yes.
While most things can't be quick-fixed, there are a few situations that I can think of where it might be helpful. Maybe the only thing that might be useful to look at is whether the "one important thing" is working or not (or worse, hurting the dancing).
Or, you might get some useful information by looking at the other couples that show up in your video. You might figure out why you keep having floorcraft issues at a certain point, for instance, from looking at how other couples travel on the floor.
There are also things you can look for that aren't happening the same time as the dancing and adjusting them won't mess with the dancing. Are you walking on/off the floor the correct way? Is your number pinned on badly?
As for myself, I don't think it would ever hurt, because I don't think I'd try to fix something that can't be fixed. But there's a small probability of it helping, so I might look at the videos if I thought it's better to do that than watch the other heats. I don't think I'd want my partner to watch videos between rounds, though...