I don't believe you get elite upgrades - their press release doesn't say anything about that.

For more info on the Continental/Alaska alliance see:

http://www.onepass.com/newpart.htm#Codeshare

http://www.continental.com/corporate/press/1999/1999-04-08-02.asp

Although - on the flights that are codeshares, and if they are ticketed as CO, but flown by Alaska, theoritically should be able to get upgrades since it is a Continental flight. Not sure though...