To answer your question in the general sense, yes - if the parent horse had two copies of the dapple gene (thus, showing dapples), it would always pass one on to its foals, making them carriers (but they wouldn't show dapples unless they got the gene from their other parent as well)

To answer your question in this specific case - the horse you've (edit: originally) linked is not dappled, sorry, but the grey layer it has does kind of mimic dapples. Using the browser's inspect tool to look at the layers, I saw that it doesn't have the dapple image layer, and that it has the grey4 greying layer. Usually a horse that is fully dappled will also say "dappled" in its color name, but since I usually try to breed away from grey I'm not quite sure if that works properly with greying horses.

(The true dapple layer also darkens the coat, for an effect a little like the sooty layer but with spots)

Oops! I linked the wrong horse!

Thank you for answering!

The horse I MEANT to put is dappled!

Ah! In that case, yes, any foals from the newly-linked horse are dapple carriers!

Also, you're welcome

Thank you so much!

One of his kiddos is for sale.