A lot can happen on the way to the Olympic Games podium and the
IOC can have some influence on that. But what happens on the podium
itself is beyond its control – as Tommie Smith, John Carlos
and Peter Norman demonstrated in their famous protest at the medal
ceremony for the 200 metres in Mexico in 1968.
So, if medallists from Russia at the next Games decide to belt
out their national anthem (or merely mouth it) in front of the
watching world while the Olympic anthem is played, all the IOC can
do (if it is so minded) is take reprisals after the event.
But taking reprisals against athletes after the event in this
scenario will not be easy for the IOC. Any such protest by Russian
athletes would be a 'national' protest, not dissimilar to
the Nazi salute given by the German athletes on the podium in 1936.
The IOC took no action against that at all because the Nazi salute
was consistent with the national character of the competition.