By very gradually increasing the level of your anaerobics over a period of years, you MAY be able to reach a point to where you can race and have a good time. Again, this depends on your individual condition. Always check with your doctor before increasing your program. I used to work with doctors on cases like this and it is the toughest coaching you can do because, if you don't know what you are doing or make a judgment error, you kill the athlete. With proper coaching and instruction, most people with problems like this can enjoy their cycling with very few if any problems.
Caution is the key word here.
To work with someone like this, I would require a direct contact with the physician. Again, Doctor Cooper's stuff is the best. I would like to say here that I find most MD's incredibly ignorant about exercise physiology and athletes. It has amazed me at how many doctors think it is a waste of time for an athlete or even a former athlete who is out of shape and over weight to have an annual checkup. This is in spite of the number of top athletes that die on the playing field every year.