OG Xbox BC - Do games on disc work if they are not available digitally in my region?

I've searched the Internet and can't find a definitive answer to this question. Most OG Xbox games are not available in my region as digital purchases (only 3 are in fact), but I understand that original disc versions of those games should still work, right?
Can anyone from Europe (or rather - from anywhere but the US) confirm that it works? I can get a copy of Ninja Gaiden Black for a reasonable price (I see it's gotten crazy on eBay though) but I'd like to be sure.