I have coronary artery disease and have had 4 heart attacks in the past 20 years. I've also led the ACA TransAm tour 4 times. One of my heart attacks occurred within months of completing a trip. Two happened about a year after completion and another occurred during the tour. I had to leave that trip in Newton KS.
Maybe just coincidence, but I cannot help but suspect that the steady diet of pizza, ice cream, peanut butter, cheese, cookies, hash browns, bacon, eggs, biscuits and gravy may have aggravated an existing condition and contributed to the attacks. When traveling with a group it's easy to chow down with everybody else thinking your normal again for the duration of the trip when you still have CAD. It' easy to say "I worked hard today and I deserve this pint of ice cream!" Yes, I think one needs and burns off the extra calories but in my case the cholesterol kept rising despite the exercise.
In conclusion, I don't think long distance cycling is bad for your health, but a typical travel diet may be risky to some if you have CAD. If you're healthy.... eat, drink, and be merry. I agree with Windrath that the exercise level of cycle touring is not particularly stressful.