Should I include translation correctness in functional testing?

We build a multi-language website. In the code, we mark English strings for translation, but the default language is our native language (Hungarian).

Should I set the default language for testing to English or Hungarian?

• If I set it to English, the tests will be closer to the code, as the test writer only need to look at the code to write the tests.
• If I set it to Hungarian, the tests will be more thorough, because they can also spot translation mistakes, missing translations, etc. But in this case, they would be more tied to the user interface, not the code. I'm not sure if this is a pro or con.

What are other advantages/disadvantages?
Has anyone experience with this?