Answer:
The labor participation rate would not change because it counts the labor force as a percentage of the total adult population, and the labor force includes both the number of people employed and the number of people unemployed, so, even if those working part-time were counted as unemployed by the BLS, they would still be part of the Labor Force.
The labor participation rate formula is:
Labor Participation Rate = (Labor Force / Total Adult Population) x 100
The unemployment rate would indeed change, because it counts the number of unemployed as a percentage of the labor force. If those working part-time were counted as unemployed by the BLS, the number of people unemployed would obviously spike.
The formula is:
Unemployment Rate = (Number of Unemployed / Labor Force) x 100