Sure. But the navy's capital shipbuilding requirements would be relatively small, and largely concentrated on hub worlds that have the TL, as well as the capacity for big ships (like Mora). No one's building dreadnaughts at Regina; even the TL15, Pop 9 hubs like Rhylanor and Glisten are probably concentrating on cruiser level contracts. It's also likely that only worlds with a Naval base actually get Naval contracts, for practical reasons (though I guess in many cases the capacity might have been present first, with the Naval base being developed later).
In a hot war situation, the Navy are likely to take over commercial yards.
In a hot war situation, the Navy are likely to take over commercial yards.