The answer to this one, is very simple.

No.

The controversy lies in methanol. At extreme levels, methanol can be highly toxic because it can be converted to formaldehyde by the liver and could potentially cause blindness if consumed in high enough amounts.

So in the real world, what does this mean?

One litre of aspartame based soda contains around 55mg of methanol. Your body can safely handle about 2000mg of methanol.

This means you’d have to consume 36 litres or around 90 cans of aspartame based soft drink to potentially encounter this risk. You will sooner have toxic effects of water, than suffer the toxic effects of methanol from consuming so much water!