Yes, but more so no.
There are actually TWO things referred to as an "egg." The first is an egg, which is a protective shell that houses some nutrients, and a zygote. That is not a single celled organism. That is closer to, say, a finger nail than an organism.
The other thing that IS a singular cell is an egg cell, which exists prior to being fertilized. When fertilized, it becomes a zygote. It's not really an organism prior to becoming a zygote(and the zygote does not stay a single cell for very long, subdividing very quickly,) but it is a singular cell.