Yes, all hyperbolic three-manifold fundamental groups can be generated by loxodromic elements.  For, suppose that $\Gamma = \{ \gamma_i \}$ is a generating set.  Take $\gamma$, a loxodromic element which is "sufficiently long" compared to the elements $\Gamma$.  Then the set $\{ \gamma \} \cup \{\gamma \cdot \gamma_i\}$ generates and consists only of loxodromic elements.  

A more delicate argument will give loxodromic generating sets, of size two, of (say) the twist knot groups.