I'm not sure why you would need a spacer. The important thing is to observe the chain line, if it's too close to the frame, then I suppose the spacer is needed.
I converted an old Raleigh from a double to a triple and the only changes that I needed to make were (aside from the crank/chainring, front and rear derailleurs) was I swapped out the 113mm bb assembly (which was loose ball bearings style to the longer axle sealed cartridge version 122.5...IIRC