Yes, no, and not exactly, a country is in Civil Disorder because no one is issuing orders. If the player returns or another player assumes control of the country by issuing orders to the countries units, it's no longer in CD and of course the units will try to do what they are told... I believe Kestas has the default form selections set as well, in case of a CD unit being displaced it should automatically disband after 24 hours, unless again, someone takes over or the original player comes back to life. Some times players will intentionally wait until just before the turn ends before assuming control of a CD'd nation, to catch potential targets off guard. Also, be ware the dirty tacticians who will refuse to finalize their orders in hopes of striking a favorable deal with a player who is taking over a CD nation in the game. Consider it a form of a temper tantrum for when things don't go their way. Personally I find the tactic distasteful, and it should be considered a form of Meta Gaming and it's not something I've ever seen allowed in any in person games.
To answer the rest, yes the game goes on, but with extreme delays as each Dip, Retreat, Creation phase will span 24 hours if a nation is in CD and has the potential to issue orders. In other words, any given Spring or Autumn can span 3 days potentially due to poor decorum. You should only allow your nation to CD if you really cannot make it to issue orders, not because your loosing.
I would like to see a penalty or a Scarlet Letter associated with players who abandon one game and continue to issue orders in another..