Would a modernized Hood survive Bismarck?

Would a late-1930s modernization of Hood change her battle with Bismarck?

Radar fire control and renewed machinery would improve Hood's performance, but the fatal shell trajectory could still occur and the exact result depends on the modernization package.

A reconstruction comparable to Renown's would give Hood radar-directed fire control, updated gunnery systems, and machinery in better condition. It could also improve subdivision and rearrange some secondary weapons and magazine spaces. Those changes might make the fatal hit less catastrophic, but they could not eliminate the chance shell trajectory created by the ship's motion and waterline geometry. Completing such a refit in the late 1930s would probably require retaining Tiger to cover Hood's place in the available battlecruiser force. The wider fleet would therefore enter the Denmark Strait scenario with different ships as well as a more capable Hood, so modernization changes several probabilities without guaranteeing her survival.