I've had alopecia for on and off for years and have also taken chemo. If it had been cancer, she wouldn't have lost just the hair on her head. She would have lost eyelashes and eyebrows. It's unlikely that smoking had any effect on that, even if it is had for her health.
Alopecia can have dozens of causes (hormones, thyroid, stress, x-rays & scans, surgery, medications, etc). It's quite obvious, from the pics I saw at the time, that she did have bald "spots." When she first shaved her head they were quite pronounced.
In her interview with Dianne Sawyer for the 700 ans Grimaldi, Albert told Ms. Sayer what caused it (I think he said stress or something?) and when the reporter confronted Caroline in the next segment, Caroline was quite cold and would not confirm it. In the same interview, Lizanne Kelly Levine said that Caroline told her simply "Aunt Lizzy, my hair started falling out and I just shaved it."
There are lots of new different medications and devices (including a laser comb) now to cure it. Caroline would have access to the cutting edge best care money could buy. It reversed itself, the Pregnancy helped stabilize an imbalance or she had a treatment regimen.