There are two possible problems:
1) The artificial sweetener by itself is very slightly cancerous. I think with the accepted data, that if you eat nothing but saccharin for 70 years you are 50% likely to get cancer from it. Of course since it isn't digestible you'd never live that long since you'd die of starvation. In real world use, you'd have to eat it for thousands and thousands of years to have a 50% chance of getting cancer from it. Thus in one of his first duties as president, George W. Bush declared it to be non cancerous.
2) Unintended chemical reactions can make cancerous products. Take aspartamine for example. It is make from benzene (a known cancer cause) and wood alcohol (known to cause blindness). No reaction goes 100% to completeness. And reactions can go in the reverse direction. Aspartamine has the tendency to revert back to low levels of benzene and wood alcohol after long periods of time and at high temperature. Thus foods made with it almost always have a expiration date, and you are never ever to cook with aspartamine. However even then it is very low levels and you are not likely to get cancer.
Basically, yes it can cause harm but the chance of it happening is so minute you might as well ignore it.