This is a really interesting question! According to wiki, 連声 is the term for Japanese sandhi (a blanket term for any phonological process that occurs across morpheme boundaries). I note this, because the examples in the question all exhibit nasal gemination (doubling of an "n"-sound), which is a (more commonly studied) subset of Japanese sandhi.
To address the second part first, I think current Japanese phonology would only allow 南欧 to surface as /nãɴ.oː/. What happens is, the /a/ gets nasalized cuz of the /n/ and becomes /ã/, and then the adjacent /n/ gets pushed back to a uvular /ɴ/ (the "n" that occurs near the back of the throat). Although /ɴ/ could theoretically geminate, modern Japanese does not allow /ɴ/ to begin a syllable, and would subsequently block the replacement of a second /ɴ/ with /n/. So that's some phonological motivation behind why 南欧 would not be pronounced as なんのう nowadays. (I lack the data to substantiate this intuition, but I feel like certain speakers might geminate the nasal anyway, but it would remain unperceived by native speakers.)
Having said that, the wiki page for 連声 gives modern examples, including
～であったら → ～だったら
私の家（うち） → わたしんち
これは参った → こりゃ参った
But these are all examples of vowel deletion (or vowel reduction), rather than that of nasal gemination (still all sandhi though). On the other hand, we also have segment insertion:
そういう事 → そうゆうこと
Where palatalization occurs to break up that long vowel cluster (/soːiu/ → /soːjiu/).
From Wiki's article on Japanese phonology, another common strategy to break up long vowel clusters is to shift the pitch and pauses, such as in 東欧を覆う(とうおうをおおう), which I suspect is a prominent feature of a scholarly paper I don't have access to.
All in all, I would say that sandhi is very much alive and well in modern Japanese phonology, although perhaps not in the restricted sense of nasal gemination.