Well, in view of batgirl's quotes, obviously Tarrasch did not, and the views of the "world tournament champion" Pillsbury or Rubinstein or Capablanca are somewhat open to question, but anyway, that does not change the fact that there probably would have needed to be more regular world championships for anyone to know for sure who was strongest.
This, again, is somewhat fraught, as one cannot discount sour grapes as a motivation for Lasker's contemporaries questioning his legitimacy as world champion.
I still believe that the best measure of his greatness is that he changed the way that chess was played. That some of his opponents accused him of deliberately playing inferior moves is an indication of how far ahead of them he actually was. As per Reb's original post, I agree that the 27 year reign is misleading and would add that it actually detracts from, rather than enhances, arguments about how good he actually was: people become fixated on the the manner in which he held the title for so long.
Well, in view of batgirl's quotes, obviously Tarrasch did not, and the views of the "world tournament champion" Pillsbury or Rubinstein or Capablanca are somewhat open to question, but anyway, that does not change the fact that there probably would have needed to be more regular world championships for anyone to know for sure who was strongest.