Sometimes.
In your first crossing, you will get birds split for the gene: One copy of yes! and one copy of not-yes. If the gene is dominant, one copy of Yes! will show in the offpsring. If yes! is recessive, it will not show, but you KNOW that it is present because the parent showed the trait.
In your 2nd crossing for a dominant gene, you typically breed back to the opposite gender parent of the breed you are working on to re-acquire any traits lost or decreased in the original cross. Since the crossing is split for Yes! (Yes! not-yes), only half the next generation (F2 generation) will retain Yes!, those that don't are removed from the breeding program.
Rather than crossing to a parent, you can instead cross to an unrelated bird displaying the characteristics you wish to re-build. If you take a number of the F1 offspring and pair with the original breed, you can vastly increase your genepool. If you pair those F3 offspring together you should get about 25% whi are Yes!Yes!, and will breed true.
If yes! is recessive, then it's best to perform at least a couple of unrelated original crosses. Then you can breed F1s together(pairing unrelated birds). You should get about 25% who receive yes!yes! and display the trait. You may need to rebuild lost characteristics by breeding these birds that display the yes! trait back to birds who don't carry yes!. Every time you do so, you will lose a copy of yes! and have to re-insert it, but you should be able to keep track of which birds have it and which don;t if you always breed the birds who are split together (or to one who shows the trait) and keep only the ones who display the trait from those crossings.