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No. A horse passes on only one copy of their gene to their baby. I don't know about genes, but a whole extra chromosome causes genetic problems like down syndrome, depending on what chromosome it is.

So if sire is kit to / kit to and dam is kit to/ kit w20 the foal will have Kit to from sire and either kit to from dam or kitw20 the dam couldnt pass on both the tobiano and the w gene.

A quick genetics lesson (I will try to make this a clear and simple as possible):

Every mammal (and other multicellular living thing) has a certain number of pairs of chromosomes. One copy of each came from its mother and the other copy came from its father. (Except in rare cases like Down Syndrome, when one chromosome has an extra copy.)

Every chromosome carries a number of genes. When egg and sperm cells are formed, the pairs of matching chromosomes divide, and each half of the chromosome set becomes part of a separate egg or sperm cell. The set of chromosomes in each egg or sperm cell will be a mixture--some will come from the father and some will come from the mother--but each will be a complete single set of chromosomes.

When a stallion is bred to a mare, one sperm and one egg will combine to create the embryo. Which of the gene copies the sire carries and which of the gene copies the dam carries get passed on to the foal is completely random, but the foal has a 50% chance of getting either gene copy from each.

Obsidian Kitsune spoke of a Punnet square. Here is a copy of one created to show the potential of getting a dead foal with two broken copies of the Kit gene.