Actually maybe some things might not work as expected – e.g. real time UI updates (if someone updated an article so that it magically re-renders while you are reading). I think the two sites would not tell each other so you would need to depend on the user refreshing their browser. There might be more. Like if you change the site settings on one site, I guess the other site would also not notice and you might need to restart the other one.
Based on Scaling up and sidekiq it seems to me that this is actually solvable. Sidekiq seems to handle it and the rest would be a matter of configuring Redis correctly.