Stage 19 and Stage 20 Question

If after stage 19 the time gap between the Tour leader and the second
place rider of the GC is only 60 seconds, will they fight for the final
placing during the final stage (stage 20) - I thought normally stage 20
are for the sprinters?

Has there ever been such a close time difference between the leader and
the second place rider in the Tour, and that the winner determined by
the final stage?