If someone quotes e.g. Leviticus 6:7, will this be the correct position no matter the language or translation?
In general, yes...
As Affable Geek answered, the divisions predate the printing press but were not part of the original texts. There aren't that many publishers of Bibles and most of them use the same system that English translations have used since Langton. So if you go to a Spanish-language service anywhere around the world, you can find your place in the text. (Assuming you understand Spanish, of course.)
It seems likely that this is for convenience and because of the network effect. Since most tools of interpretation (dictionaries, commentaries, concordances, etc.) use the standard system, most people who purchase a Bible will expect to find it to be compatible to that system. A publisher would quickly go out of business if they tried to introduce a novel system.
with two exceptions.
As it turns out, Leviticus 6:7 is not the same between the Christian system and the Jewish system:
It turns out the Jewish system puts what we call Leviticus 6:1-7 into the end of chapter 5 as verses 20 to 26.
Psalms 88:5 in King James Version:
Psalms 88:5 in Jewish Publication Society (based on versification in Masoretic text):
Even some verses differ in NT according to which Greek manuscript you are reading from.
Yes, generally, though not universally.
While definitely a respected theologian (he was an Archbishop!), his "sense"-based structure is by no means universal agreed upon. Indeed, there is an apocryphal tale underlying the seeming lack of any rhyme or reason in the structure that suggests Langton was riding his horse as he inserted the numbers. The story goes that when his horse's feet touched the ground, he inserted a verse, and when he fell off the horse, he inserted a chapter!
Other versification schemes exist, but his is the most common. Manuscripts that predate this convention are sometimes back-versed, and some translations have reversed the scripts, but most popular translations, such as the KJV, NIV, NASB, RSV, ESV, NLT, etc... all use Langton's schemes.
Indeed, the versification is so well received that as modern manuscripts cast doubt on the authenticity of some verses (see 1 John 5:7), many modern translations will omit the verse altogether, going directly from 6 to 8.
Internationally, those that choose to follow this pretty well received convention tend to follow it as well.