In single player the Overload ability seems to ALWAYS completely remove the target's shield. So I ask then, what is the value of leveling up the damage of the ability if I only want to use it to remove shields (using incinerate to do damage after the shield has been destroyed)? Should I take the recharge speed upgrades if shield removal is my only intended use?
If your main use is to remove the Shield or Barrier, it's indeed best to take the recharge speed upgrade, or the multiple overload bonus.
Don't forget that overload do also damages to the synthetics!
Negative. Unless you grab full damage on it, playing on Insanity will not drain a lot of the low level shields instantly. Tested with Garrus and EDI on multiple playthroughs, EDI having max damage and Garrus having Chain Overload.