The issue here really is one ...

The issue here really is one of Hardness.  The hardness from the regen will precipitate if either the temperature is increased such as from blowdown or the pH or carbonate concentrations are increased .  

The Softener could be combined with the blowdown only if the blowdown was cooled to room temp prior to mixing with the high hardness water form the softener.  this may be done with softened quenching water or exchangers for capture of the heat.

As for the Dealk it depends which type of dealk you are using.  Weak Acid Cation, or Split stream would not cause issues with a softener, however if you are using a Cl Anion and are regenerating with salt and caustic, you could likely have some issues if both systems were to regenerate at the same time. You would have high hardness and high pH/Alkalinity which is a recipe for scale formation and potentially big issues.

another factor to consider would be other flows in the same drain that could be a diluting factor.

Hope this helps