When you pop the hood on my swap you're gonna see 3.8L's of Gen 5 Whipple madness on top paint matched to the car.That was what my reservations were. When you pop the hood on a terminator, you see the iconic blown 4.6 engine. Pop the hood on a coyote and see that flimsy plastic 5.0 engine cover (Yes, I know you can take it off). Although, reading more, the IRS was already swapped out for SRA. At this point, the car is just a body to house an engine, it is not really a stock terminator that is being gutted for a Coyote, it is already almost there. The only thing the Coyote does worse, in my opinion, is sound. I don't like it.
As an owner of two old beaters from the muscle car era that are not in original configuration, I should understand. My Mach 1 has a 351C in it right now as the 351W died years ago. Its rebuildable, but a Cleveland was a much better stock engine in the power department than the Wheezer. Someone swapped the heavy cast iron FMX for a 4spd toploader at some point in its life also. My Charger has a non-original engine block and transmission in it right now. Of course these cars are worth a lot more all original, but non-original means I can mess with the cars a little and not really hurt their value.
Tl;DR: If it is close to original, say bolt ons, I would leave the car alone. If it isn't, then modify away. It sounds like the car is already beyond bolt ons.