You could use that sentence, but I don't think it would have the meaning you want it to have. I've compared different tenses with their meanings (as I see them).
The Korean war is having a bad effect on my family. (present continuous)
The Korean war is ongoing and is currently affecting my family.
The Korean war has had a bad effect on my family. (present perfect)
The Korean war is ongoing and has, in the past, negatively affected my family. It may continue to have a negative effect in future.
The Korean war had a bad effect on my family. (simple past)
The Korean war is over, and in the past negatively affected my family. Those effects may still be being felt.
The Korean war had had a bad effect on my family. (past perfect)
The Korean war is over, and in the past negatively affected my family. Those effects are no longer being felt.
To paraphrase the British Council, the perfect present is used:
- For something happening now that started in the past
- For something happening again now that has happened multiple times before
- For your experience up until now
The common theme here is that everything expressed with the present perfect continues to happen. If what is being expressed is no longer happening, the simple past or past perfect are better choices.
The difference between simple and perfect pasts in this case is slight (compare sentences #3 and #4 in my answer). In this case, the perfect past definitively states that the effects are no longer felt, while the simple past is ambiguous – they may or may not continue to be felt.
If you're unsure, the simple past will probably be the safe option.
If you want to express that the Korean war is over but its repercussions are still felt (which I think you do), you could use the simple past. However, I think it would be more idiomatic to say one of:
The Korean war had and continues to have a bad effect on my family.
This sentence explicitly shows that the war is over but that it is still having an effect on your family.
The Korean war still badly affects my family.
Use of the adverb still here shows that the war continues to have an effect, and it is implied that the war is over.