I tried looking up the word "corps" on dictionary.reference.com and it says it's pronounced "kawr", "kohr", "kawrs", or "kohrs", none of which match the way I've always pronounced it with the "ps" sound. I have always been a little leery saying it this way because it sounds like a dead body, and if you're talking about the Marine Corps then this isn't the best mental image.
"Corps" and "corpse" both have the same ultimate origin in Latin "corpus" (body).
The former derives from the Latin via Medieval French, as far as I know. The French pronunciation "korr" (or slightly Anglicised to "kohr" or even "kore") is thus the historically correct pronunciation.
Pronouncing it in any way ending with an "s" is not advisable. It certainly won't give others the impression that you're educated. (Worst of all is "corpse" - please never say it like that.)