My dictionary lists the pronunciation of corps as [kɔːʳ], [kɔrz]. So, I am wondering if native speakers really pronounce the s sound?
Corps is normatively pronounced with the sound [z] in its plural form, but not in its singular form. Corps and core are homophones.
In a rhotic accent, corps is pronounced as [kɔr] or [kor] in the singular and [kɔrz] or [korz] in the plural. (It has the same rhotic vowel as the word force; there is variation between accents in the quality of this vowel and in whether or not it is identical to the rhotic vowel in the word north.)
In a non-rhotic accent, corps is pronounced as [kɔː] in the singular when it comes before a word that starts with a consonant. It may be pronounced as [kɔːr] when it comes before a word that starts with a vowel, depending on how connected the two words are in speech. (The transcription "[kɔːʳ]" is a shorthand for "[kɔː] or [kɔːr], depending on the context".) It is pronounced as [kɔːz] in the plural, with no [r] sound.
(All of these are broad, not narrow transcriptions: a number of phonetic details are left out. E.g. phonetically, the vowel in a non-rhotic pronunciation may be closer to IPA cardinal 7, [oː], than to IPA cardinal 6.)