Would you sell someone a new car without an engine and put the old engine from their old car in the new one?
Creating a Frankenstein monster system is certainly not doing someone with money problems any favors. What the hell good is a new unit that is most likely going to operate less efficiently then it was intended, have possible issues from the effect of the existing coil and not last as long as it was intended?
An HVAC system is a singular system that just happend to be in two parts that just happen to be seperated from each other. Think of the indoor coil as a head, the outdoor unit as a body and the lineset as a really long, skinny neck. Putting the wrong head on a body is creating a monster.