I don’t see why it would be unhealthy. However, I know that it is harder to breastfeed for obese people, I’ve read several studies looking at different reasons but they all pointed to decreased lactation and/or difficulty with latching for the babies.
If a morbidly obese woman survived pregnancy and childbirth to deliver a healthy, living newborn, if that didn’t kill her, then they are both pretty much home free as far as breastfeeding is concerned I would think.
The only thing that would make breastfeeding unhealthy is if the mother was ingesting drugs or alcohol or harmful prescriptions that will pass through the breast milk.