Can life occur from a fertilised egg cell, in which both the egg and sperm possess an extra copy of a chromosome?
There are many ways to answer your question, I'll try a couple.

First, extra chromosomes in humans are commonly deleterious. However, there are known rare forms of tetrasomy that are not lethal, see Wikipedia on tetrasomy. Note that the causes of tetrasomy are rare events, so they are typically occurring in just one of the original gametes, not both; for it to happen in both would require a rare event paired with another rare event - not saying this is impossible, just less likely.

Polyploidy in other organisms, particularly plants, is both common and normal, see Wikipedia on polyploidy.