Would building Soviet battleships leave less armor for tank production?
Short answerBattleship armor required a different production process, while expanded cruiser-armor capacity could also supply tanks. A larger navy would still take money from other programs.
NotesBattleship armor and tank armor require different thicknesses and manufacturing processes. Soviet cruiser armor came from plant more comparable to that used for tank armor. Expanding this part of the naval industrial base could therefore leave the Soviet Union with more capacity to manufacture tank armor during the 1930s. That possible benefit does not remove the cost of the ships themselves. The wider effect would depend on which other investments Stalin reduced, and his priorities cannot be predicted confidently.