Actually no this is not the case....
A Dominant mutation still can only pass on one copy of the gene to the offspring.
Dominant mutations are visually identical wether they are heterozygous or homozygous carriers of the gene
If the parent is a Heterozygous Dominant gene carrier bred to normal Statistically 50% of the offspring will be Heterozygous carriers (Visual) and 50% will not be carriers (completely normal)
If the parent is a Homozygous Dominant gene carrier bred to normal
All offspring will be Heterozygous cariers of the gene. Thus they will look identical to the Parent Homozygous carrier but only be heterozygous carriers themselves (1 copy of the gene)