After cold crashing my cider, can I backsweeten with Pasturized cider to improve the flavor AND kill the remaining yeast? I know that pasturized cider doesn't ferment.
Only the yeast in the pasteurized cider will be dead.
There will still be yeast in your cold crashed cider.
That yeast will eat any sugars left over in your bottles.
Pasteurization info here http://en.wikipedia.org/wiki/Pasteurization
If the yeast in the pasteurized cider was actually killed chemically (like with potassium sorbate) it's not really pasteurized, I don't think.
Regardless of what we should call it (I don't know offhand) the chemical that killed the yeast would probably still be around in the "pasteurized" cider. When you add it to the cider with the active yeast the chemical would be diluted and (probably) ineffective. That's going to depend on concentration.