Would more colonial yards repair capital ships?

Would stronger colonial shipyards have allowed the Royal Navy to send major battlecruisers overseas for reconstruction?

Not without much greater investment; the realistic gain was local major repair of cruisers and smaller ships, not full capital-ship reconstruction.

Useful dispersed capacity stopped well short of full capital-ship support. Commonwealth yards capable of major cruiser repairs would shorten deployments and reduce bottlenecks at the few largest bases. That distributed repair network would still materially improve fleet availability. A 48,000-ton battlecruiser or fleet carrier demanded dry docks and machinery on another level.