Not in most cases. Very rarely, you will find a silver-based Leghorn hen, but 99% are Dominant White instead. 100% of their chicks from any cross will be mostly white with some color leakage.
Black Sex Links are made from a cross of a Barred hen with any non-white, non-Barred cock (though Red roosters are most often used and depending on the rooster not all color patterns will be sexable at hatch). Commercial BSLs are made using a Rhode Island cock with a Barred Plymouth Rock hen.
There's no such thing as a "gold sex link." Do you mean Red Sex Links? Red Sex Links are made from a cross of a Silver hen with a Red or gold rooster (some other colors can be used but they are often not sexable at hatch). Commercial RSLs are made using a Rhode Island cock with a Delaware hen.
Oh you know what I was being an idiot. "Gold Sex Link" is what some hatcheries call Red Sex Links. I'm so used to calling them RSLs I forgot some people still use the Gold name. Genetically and practically they're the same thing.
Yes, the progeny of your mom's birds will be Black Sex Links.