bendy-ness appears to come easier for yogis with a more regular practice, but flexibility is a huge benefit that everyone can gain from yoga.
even if you are 'not flexible at all,' yoga can increase your flexibility. just remember that your breath is the most important part of your practice (read: if you stop breathing you will pass out), so if you find yourself going too far in a pose that breathing becomes difficult, simply back out of the pose (read: yoga can be a case of where less is more). when you find ease in your body, mind and breath, in whatever pretzel-twisty posture you might find yourself in, that's the good stuff.
in the meantime, if you want to touch your toes sooner - try bending your knees (instead of rounding your back) when you are doing poses like standing and seated forward bends, it can help in down dog too.