The TTI headers do not wrap under the drag link.
Yes the engine can be installed with the transmission attached, but it may not be easier?
If installing from under the car with the K-member removed like the factory did it, it would be easy. If installing from above, you need an engine hoist that can go pretty hugh because you have to tilt so the transmission hangs down, then when the tail shaft gets close to the ground I usually place it on the floor jack so it can roll back under the car. Usually this will start to level the engine as it goes further into the engine compartment, and the front accessories/pulleys might want to hang up on the radiator support (best to remove them first.)