I bought the ME1 PC version just a few days ago so it came with the patch when I downloaded it. I did try to reinstall the patch just to see what would happen, couldn't hurt right, and that's when I got the message the game couldn't be found.
There were a couple more steps in the 'fix'. The rep removed the game from Origin. I redeemed a new game code through the old EA site, and the game transferred from there back to my Origin Client account.
The game won't work for me if it's launch through Origin. It does work with the desktop shortcut and run as admin method though. I'm not sure that info helps or not.
However, back to your question, I did not have the MassEffectLauncher.exe before I contacted the EA rep.