I was thinking that since kids mostly don't remember anything from before age 2-3, it wouldn't matter. But then again, it probably would matter to the parents, who wouldn't want to distress their kid regardless of whether he remembers.
The kid will definitely realize mom and dad are gone at two, they're not vegetables, but whether that has any impact on them later is not something that's been established by evidence. The idea that kids are the "sum of their experiences up to that point in time" is an old wives' tale.
http://www.slate.com/articles/life/family/2012/04/children_s...
Far from having no memories at all, very young children remember a lot like adults. In early infancy, the neural structures crucial for memory are coming online: the hippocampus, which is, very roughly, in charge of storing new memories; and the prefrontal cortex, which is, very roughly, in charge of retrieving those memories.
But these neural regions and their connecting pathways are still developing. And they capture only part of the present as it flows by.