The answer is yes. H_{2}SO_{4} is a very strong acid, it has an acidity constant much higher than 1 (it's very difficult to measure it in water because it's almost totally dissociated in its first dissociation) while H_{2}SO_{3} is a weak acid, with acidity constant = 1.4*10^{-2}.

Just think that the associated base of H_{2}SO_{4}, that is the ion HSO_{4}^{-}, is practically as acid as H_{2}SO_{3} (Ka = 1*10^{-2})...