More specifically did it's popular association with Satan/the Anti-Christ predate the introdution of Arabic numerals and if so how would it have been represented in Roman Numerals? As VI VI VI or DCLXVI? I ask this because in modern American English we refer to it as six six six rather than six hundred and sixty-six.
Well, it's in the Bible to answer your first question.
Revelation 13:16-18 says as part of a prediction about the end of days:
[16] And he causeth all, both small and great, rich and poor, free and bond, to receive a mark in their right hand, or in their foreheads: [17] And that no man might buy or sell, save he that had the mark, or the name of the beast, or the number of his name. [18] Here is wisdom. Let him that hath understanding count the number of the beast: for it is the number of a man; and his number is Six hundred threescore and six.
The entry on the site there provides a number of alternative translations, but the King James Version quoted above is the oldest there. Other translations variously render it as "666" and "six hundred [and] sixty six".
Meanwhile over at www.biblestudytools.com, a version of verse 18 in the Latin Vulgate reads:
18 hic sapientia est qui habet intellectum conputet numerum bestiae numerus enim hominis est et numerus eius est sescenti sexaginta sex.
(emphasis mine)
So while I can't answer definitively to how it would have been represented in roman numerals, it would seem that the important thing here is the number of six hundred and sixty-six, rather than the digits six-six-six.
The 19th century Pulpit Commentary (linked from the biblehub page above) notes that no-one really knows what the writer is getting at with the whole 666 thing, but makes a comment about the form in Greek which it would have originally been written in. I don't read Greek, so I can't really comment further on the contents of this:
And his number is Six hundred three score and six. The Revised Version is better, Six hundred and sixty and six; it preserves the similarity of form which is found in the Greek words, ἑξακόσιοι ἑξήκοντα ἕξ, as found in A. In א we have ἑξακόσιαι, etc.; in P, Andreas, ἑξακόσια. The shortened form χξς' is found in B and most cursives. C, 11, and some manuscripts known to Irenaeus and Tichonius differ by reading ἑξακόσιαι δέκα ἕξ, "six hundred and sixteen," but this is probably incorrect.