Given how many weird things I've heard with the lady's pronunciation (mostly like sounding the s in "plus tard" and other random words) so far I wouldn't be surprised at anything she does or doesn't do. She has a beautiful voice, but these things are strange. I lived in Paris for a year and I never heard a native speaker sound the s in "plus tard".
No, the plural of "ce chien" is "ces chiens".
"ces" is the masculine or feminine, plural demonstrative adjective.
- ce, masculine in front of a word starting with a consonant sound: ce chien
- cet, masculine in front of a word starting with a fowel sound: cet ami, cet homme
- cette, feminine singular, all nouns: cette chienne, cette amie, cette habitude