Let $M$ be a sub-Riemannian space. 
Consider a smooth curve $\gamma:[0,1]\to M$ such that 
$\dot\gamma(t)\not\in  H_{\gamma(t)}$, where $H_{\gamma(t)}$ is the horizontal subbundle ( i.e. $\gamma$ is totally non-horizontal curve).

Is it obvious that the curve is not rectifiable or has infinite length?
I haven't found any mentions about this questions.