I have consulted a couple of guys who try to shave only the minimal amount of hair and integrate some of their "unhealthy" hair, but in my opinion it isn't worth messing with. They usually end up using concealers and eventually have to shave more and more hair as their hairloss continues.

There might be certain circumstances where you would be better off working with some hair that is questionable, such as if it means having to use a drastically larger unit but as a general rule it's usually better to shave off all of the unruly stuff. It's a psychological thing. The way I see it once you are committed you might as well take off as much as you need to make it look the best it can.