Well, this is interesting. I think I would say no.
One can only be fully mindful when the five hindrances are not active. This means there is also no craving (or at least no sensual craving) because this is one of the hindrances.
here is the case where a monk remains focused on the body in & of itself — ardent, alert, & mindful — putting aside greed & distress with reference to the world.
However, with less mindfulness it is still possible to see the craving. It doesn't mean all mindfulness is gone immediately when one of the hindrances knocks at the door. This is partly why the hindrances are also a foundation of mindfulness (satipatthana sutta), I think. Of course you can also reflect on the hindrances when they are gone.
Thank you. This is the angle from which I was asking my original question but the other posts also highlighted some very important and well thought out points.
I've been in a cycle lately where I've been bothered by craving and other stresses quite a bit. I've noticed that as long as I'm focused on the now, the task at hand, I spend less of my day craving, which of course then, means the day is a lot more pleasant. I've also noticed that what happens immediately as I lose mindfulness (or maybe a better term would be concentration) is that the mind-movie or chatter starts running in the head. If I notice that dreamworld for what it is, I can get right back to the breath, the body, or whatever object of observation and I become more at ease.
In regards to some other posts, I've had some nasty dental work done over the past six months or so. When I'm in the chair and the 10 numbing needles are jammed throughout the gum line, I found if I just concentrate on the pain, it's not really so bad. Of course, I suppose I could try the whole procedure without pain-killers or numbing agents but I'm not there yet.
However, I am finding craving a bit more slippery. Where I have the willpower to deal with pain, I don't have the same with craving. I'm having a hard time staying with the feeling of craving or even clearly seeing it. I just know it's there and it gets annoying. It's a little pest until it gets fed, so to speak. So, in order just have a more peaceful mind I've been finding mindfulness really helps in this role. In the past I viewed the role of mindfulness as one in which to cultivate insight, and I'm not minimizing that fact in any way, but it also seems to have additional benefits. For me the practical, daily refuge in mindfulness is a worthy enough goal.
"To avoid all evil, to cultivate good, and to cleanse one's mind — this is the teaching of the Buddhas" - Dhammapada 183