Tsushima and the human cost of fighting only for the flag

Are there naval engagements where one side would have been better surrendering before battle?

Yes; Tsushima is a strong example, although honour and command culture made an early Russian surrender extremely unlikely.

Surrender before the Battle of Tsushima could have preserved lives, although Admiral Rozhestvensky was never likely to choose it. The same problem applies to ships that continued firing solely for the honour of the flag despite overwhelming odds. Such conduct can inspire respect for courage while still raising questions about responsibility to the crew. Personal or institutional honour needs to be distinguished from operational purpose.