Using a tilt shift lens on a star tracker

My first thought would be that whilst you're moving the camera to track the stars, you're going to generate a 4-minute blur of the landscape.

I'd be tempted to take another static exposure to get the landscape & just matte the two together later. Get more sky in the tracker shot than you need for the composite, so you don't get any landscape in the crossover area.

With regards to shift, there isn't anything to be concerned about. After all, a shot with a shifted lens is essentially the same as just a crop of an image taken with a larger sensor/film size and a correspondingly Wider angle lens.

From a minor-details point of view, using the shift lens to prevent the apparent "lean" of vertical objects like trees, when shooting on a tracker, it really depends on your local azimuth. Because you're shifting upwards, you will be emphasizing the motion of the scene in the extremes towards the shift direction, and relative to the center of the frame, de-emphasizing the motion of elements that are closer to the unshifted direction. Meaning, you will see exaggerated star motion in the top and top corners of the image, and the motion of the trees and landscape will appear less exaggerated (relative to the center of the image, which of course is shifted upwards).

Just keep the amount of shift consistent and shoot away. No worries unless you alter the lens' shift angle.