SO2 turns lime water milky.
CaSO3 is also a white ppt. insoluble in water. Therefore, yes, it will turn limewater milky.
This is the same principle as to carbon dioxide:
Calcium sulfite is insoluble, thus precipitating, in saturated Ca(OH)2 solution.
Ca2++2OH−+SO2→CaSO3,precip.+H2O
Compare:
Ca2++2OH−+CO2→CaCO3,precip.+H2O