Yes it can unless you are flat lining shooting at an animal. Your total body reaction to not only seeing an animal but settling in for shot is an exciting endeavor to say the least. Blood vessels expanding, contracting, respiration rate jumps, heart rate jumps, your chest is moving pretty good prob after the shot. The stress on installed blood vessel grafts and sternum will be significant. Only his cardiologist knows if and how much damage was done to his heart from the heart attack. FYI heart attacks can damage the heart such it may take long time to recover from the damage or the heart is left with reduced capacity. This is not a broken leg that just heals up as good as new. Every heart attack is different on how and what occurs during and in aftermath. I was lucky with no damage identified with several ultrasound evaluations 3-6 months after recovery. "It's just hunting" and if you cannot realistically and SAFELY hunt this year, do the work to insure you can the following year with PT, commitment to exercise and yes, diet changes. You will hit ground "running" with much better physicality and enjoyment. Your mental condition will also benefit.Dont be shocked when your Cardiologist puts you on a treadmill within a couple of months following your surgery.
I called my surgeon and wanted his opinion on that, and he said go for it.
Can hiking around hunting be any worse?
There are things you can do to enjoy our sport. Build a rifle, prep a gazillion brass, update reloading equipment, "hunt" down reloading components etc.
The OP was aware of his potential and thankfully did not ignore symptoms. Many do not and are no longer with us.
BTW If your heart rate isn't affected by hunting, take up checkers.