I believe what you are asking about is water intoxication.
To answer your question simply, yes, too much water, especially in a very short amount of time, can lower sodium levels for an 11 month old, an 11 year old, or pretty much anyone at any age. Babies younger than 6 months and athletes are the most vulnerable. Symptoms of water intoxication are (to name a few) drowsiness, confusion, weakness, fluttering eyelids, and, seizures. Besides age and activity level (in the case of athletes) the other factor that increases risk is a recent bout of diarrhea or any other illness that causes dehydration. Since your child is older than 6 months, is not a marathon runner, and (I assume) has not had a recent illness, he is therefore highly unlikely to be at risk for water intoxication, which very rarely affects "normal" people.
Based on your statement that your child is drinking 1 liter a day and the recommendation of 1.3 liters of total fluid intake for a child his age (which includes the water that is in food and other sources) I doubt your baby is drinking enough to put him at risk.
The only thing that may be an issue is the loss of appetite that can result from a belly full of water which would perhaps prevent your child from getting enough vitamins and minerals because he's not eating as much, but honestly, this seems to be a stretch.
I would say that if your baby is otherwise healthy, gaining weight, and happy, his water consumption probably isn't anything to be worried about.