Hi JoHon,
Yes, this works the way you want it to.
Kalitas causes a replacement effect to trigger when ever a creature an opponent controls dies. As you rightly say, this means that when you sacrifice
Generator Servant, it will be exiled.
However,
Generator Servant's mana ability doesn't require it to die to trigger, it simply requires you to sacrifice
Generator Servant as part of its cost. You will still get the two colourless mana and if you use it on a creature, it will still get haste for the turn.
If we compare it to something like
Doomed Dissenter, we can see an example of wording where a creature specifically needs to die (i.e. hit the graveyard) for its ability to trigger.
Hope this helps.