Yes, that's correct - fatty tissue buildup does make it more difficult for the heart to do its job.
Congestion caused by fatty tissue in the heart can result ins omething called Coronary heart disease (CHD), a disease that can be considered one of the biggest killers worldwide.
The condition develops when blood flow through the coronary arteries is blocked up by fatty tissue, and this prevents blood supply to vital heart tissue and muscle.
If you feel like you might be in danger of suffering from heart complications due to a fatty tissue buildup, then you should really speak to a medical professional to better understand actions you can take, and lifestyle changes you can implement to improve your prognosis.