I think everyone probaby has something they don't like about themsleves, but that doesn't necessarily mean they people cannot simply accept themselves and be confident without actually liking every part of themselves. So yes I think it's possible to not be self conscious.
Questioning and being honest with yourself, even about negative things, is way different than being self-conscious.
I definitely used to be rather self conscious but I'm not at all anymore. I still have those days where I feel "blah" but I've come to accept my curves and I think I'm a babe :p Plus I know that I know what I'm doing so I always feel really confident in bed. Everybody should learn to love themselves!!!! It's a slow process but if you focus on acceptance the self-consciousness will gradually disappear.
There's parts of me I don't love, for instance when some acne appears, or when I think I look kind of blah after a long night, however I love myself and my body, who I am inside, and on the outside. I think that's the most important thing. Even if you DO hate something about yourself, try to learn to love that, and all other, parts.
I think everyone is self-conscious about something. The more you love yourself, the less you care about what other people think. Each of us was made to be an amazing and beautiful person, sometimes we just get caught up in how the world views us. As I got older, I realized that those people who judge me are not the ones who really matter anyway. In fact, they were the ones that made my life better by leaving it.