According to TKD, qIppu'bogh yaS vIlegh means "I see the officer who hit him/her" and yaS qIppu'bogh vIlegh means "I see the officer whom he/she hit", so can you say something like be'Hom qIppu'bogh yaS vIlegh, and if so, does it mean "I see the girl the officer hit" or "I see the officer who hit the girl"?

Yes. :)

You can say that, and it means both of those things. Context will tell the listener or reader which one you mean.

There is an optional way to disambiguate the two meanings, which is not explained in The Klingon Dictionary, but which Marc Okrand has told us elsewhere: you can add the noun suffix -'e' to the head noun of the relative clause to show that it is the head noun.

be'Hom'e' qIppu'bogh yaS vIlegh
I see the girl whom the officer hit

be'Hom qIppu'bogh yaS'e' vIlegh
I see the officer who hit the girl

-- 
SuStel
http://trimboli.name