Origin is not going to detect Spore if it was not bought from Origin.
To patch Spore, simply launch Spore, log in, and if you have not already patched, a window will pop up asking if you want to install the lastest patch. Hit yes and let it patch. Follow any steps that an installer window might say to do if one pops up. Sometimes you have to patch 2-3 times until you have the latest patch.