I am going to go out on a limb and say yes, gunners would be warriors. Since the leaders/commanders of dropships, jumpships, and warships are warriors. That said, there would be a few caveats. Since some warrior Bloodnames have specialized in naval combat, there should be large numbers from the sibkos of said Bloodnames. I do not logically see how a Trial of Position would allow a cadet to assume command of a warship or Star of warships. Dropship, jumpship, and warship command should require a different level of warrior training/learning from their Mech/Aero/Tank counterparts. If we take our current blue-water navies as an example, do cadets graduate right into command of a U.S. carrier? No, so why would the Clans do so? Instead, I propose a Clan naval career takes a longer path to top tier success as compared to the other warrior paths. This would explain why Khanship in most Clans is dominated by non-naval warrior types.
Anyway, naval sibko graduates would/should be assigned gunnery positions and work up the chain of command. Some (most) would never rise further. Others would rise and find their niche in commanding certain types of dropships, jumpships, or warships. Some of these would compete with former aerospace warriors. The best would slowly rise to command the best warship or fleet the Clan has to offer.
At the end, gunners would be warriors. Some would be the best and rise. Others would find their niche and stay in one spot. Still others would be bounced around by their commanders to areas where they could do no harm (Caine Mutiny).