Chicago "L" cars would look out of place, but the standard North Shore interurban car looks a lot like a Pacific Electric 1200-class car, and there should be at least one available. Install roof-mounted destination signs and PE air whistles, paint it in a PE paint job, number it 1270 and away we go. (We now return to the land of reality.)
"Impossible" may be a bit too strong a term, but "highly unlikely" is probably fairly close. Back in 1970, I worked in San Bernardino, and would see preserved Santa Fe steam locomotive 3751 sitting in the park near the depot, cold, silent and motionless. Had someone said, "22 years from now, you'll be riding behind this engine from Barstow to Los Angeles," I'd be tempted to ask, "What have you been smoking lately?" And railfans are looking forward to seeing this engine steaming again in the near future. So, it's not impossible to have vintage electric cars on the Metro light rail lines, but I'm not holding my breath or betting the ranch either.