We don't know to what extent the damage was, however. Destroyed could be an exaggeration for all we know. All that could've happened was the debris from the Halo would've crashed onto the Ark, and parts of the Halo could still be in space, undamaged.
Cortana said and I quote, "When the ring fired it shook itself to pieces." I'm pretty sure that the Halo in Avalanche is quite intact. Also, the damaged Halo obviously did enough damage to the Ark to cause the portal to destabilize and close.
So I?m pretty sure taking into account both of these reasons that the multiplayer does not
take place after Halo 3. For the ark to have been damaged, the Halo would have to have been broken significantly. It is not on Avalanche; therefore Halo 3 multiplayer does not
take place after the single player.