Application of UKF on quaternions
Yes, it's perfectly possible.  All that you'll need is to model how you think the angular velocity components of the state will evolve.  Usually simple brownian (random) motion is enough, at least to start with.  If you know more about how the angular velocities are constrained, then you can include that in the model.

All that it means is there are no outputs from your signal model directly from those elements of the state.

For example, in this answer to another question the state is made up of the $x$ position and the $x$ velocity, but there is no velocity measurement.  

$$
\begin{align*}
\mathbf{x}_{k}  &amp; =\left(\begin{array}[c]{c}x_{k}\\
\dot{x}_{k}\end{array}
\right)  
\end{align*}
$$

All that means is the output matrix $H$ zeros out that part of the state when producing the measurement.