While the outcome of a bicycle race is more about the fitness level of the rider than their mount, (there is no such thing as a “Fast Bike,” they will just sit there, stationary forever, until you get on and feed them some of your energy.) it certainly does help to have a competitive bicycle when you enter a race. Still, no one ever did or would enter a major race on your commuter/tourist Legnano, it is a nice and attractive bicycle but it is not the last word in lightweight quality construction and its relationship to a Tour or Giro winning bicycle is somewhat akin to the relationship between a Schwinn New World Lightweight and a six day Paramount.
If you are looking for a top end period ride, compare your Legnano to a Prewar Paramount Tourist with components designed and manufactured by Schwinn to equal anything available in the world at that time. I think you will find that Schwinn achieved their goal handily and that their companion, second tier, Superior is at the least equal to (and arguably superior to) a standard tourist Legnano of the time.