I'm not sure if it's the same for all breeds, but in silkies, to express mottled, it takes two genes. You putting your mottleds together provided they look mottled will be all mottled chicks, and should pan out the way you mentioned.
If you bred your chocolate mottled with a chocolate hen with no mottled gene, you'd get chocolate chicks split to mottled. They won't show it though. When those get bred together, you'd get mottled chicks.
A chocolate rooster with a black hen would produce sex-linked chicks. The black ones will be cockerels split to chocolate, and the chocolates will be females.
As for a single mottled gene bird with a white with zero mottled, I'm thinking you won't get any mottled the first generation but some would have a mottled gene. The mottled in single gened birds shows up when they're chicks, but disappears. So then you could breed two of those and get mottled chicks.
There are a few things that are in play though, for instance, a black silkie rooster I have, (split chocolate, 1 mottled gene) with a chocolate hen (1 mottled gene). I expect to get a mix of chocolates & blacks (split to chocolate) sex-linked carrying 1 mottled, chocolate mottled, and black mottled. An oddball blue could come out of this too. It's an experiment for me. She's due to lay any day.