Would the Royal Navy still hunt Bismarck if Hood survived?

If Hood were badly damaged rather than sunk, would the Royal Navy pursue Bismarck as aggressively?

Yes; Bismarck still had to be destroyed, although Hood's survival would create a major post-battle reconstruction decision.

The fleet was already concentrating against Bismarck, so Hood's survival would leave the main operational reason for the pursuit intact. Hood's loss gave politicians an immediate explanation for the extraordinary concentration of forces. Without the sinking, some ships might show less willingness to disregard orders in joining the chase, although the answer still expects a determined pursuit. The larger change would come afterward: rebuilding a badly damaged Hood would probably take the place of Vanguard in the construction program.