Yes, the implication here is that the light from quasars can be seen after the quasar has burned out.
For anything that far away to appear from earth (AFE), it would have to produce more light than 90 billion suns (90B).
AFE - - - - - - - > 90B
Nothing that burns at that rate (90B) can exist for more than 100 million years (100M).
90B - - - - - - - - - - - - > <100M
From this, we know that quasars can't exist for longer than 100 million years. But if their light takes 500 million years to reach earth, then we are only seeing dead quasars.