In a nutshell? No. That is the very last place I want to see that deer. (Heading away, across open water, swimming.) I will not take that shot. Could I do a head shot, sure, I have before. Would I do it here? No, why? He is too lean to float, he will sink like a rock. That means diving to recover a body in ice cold, moving water. He could drift for miles. If I cared about the mount, it would be ruined. The meat would likely be wasted by not finding him, and low temps could cause hypothermia and even death to the unprepared diver.
I will let him go, watch him for next time, and plan out a method for getting him before or after the river.
Never shoot a swimming deer. It is way too much work if you are lucky, and wasted if you are not.
The only real difference between a good tracker and a bad tracker is observation. All the same data is present for both. The rest is understanding what you are seeing.