That's correct to some extent, but it does require the context to be obvious; usually in the sense that the body part belongs to the subject of the sentence.
Jeg har vondt i hodet (mitt).
Han har vondt i halsen (sin).
Hun har brukket benet (sitt).
Here, there is no subject, and the neck could belong to a giraffe for all we know. So, instead of guessing wildly, we play it safe with the definite form.
The throat is on the inside of your "hals/neck"; it's the passage that goes from your mouth and down toward your stomach. The outside, where you'd place a scarf, would be referred to as "the neck".
Mark "the throat" can be a translation of "halsen", but only if that's the part of it you're referring to. For example, if you have a sore throat, you'd say that you "har vondt i halsen".