Probably, and yes.
The yes is about sexlinks-- yes you can cross a not-barred rooster with any hen that has the barring gene (including cuckoo), to get sons with barring and daughters with no barring. Depending on the color of the rooster, the barring on the chicks might be easier or harder to spot. (Easy on black chicks, almost impossible if the chicks also have Dominant White that turns black to white: white barring on a white chick! Barring on splash or buff is also hard to see.)
For producing Silkied Easter Eggers:
the "silkied" part will breed true, so crossing the rooster to Silkie hens will give 100% chicks with silkie-type feathers.
As regards egg color, if the rooster has two copies of the blue egg gene, you can cross him with any hen and get chicks that all have one copy of the blue egg gene, which means the daughters will lay blue or green eggs.
If the rooster has only one copy of the blue egg gene (like the chicks in the above paragraph), then he will give that to half his chicks, and the other half of his chicks will inherit the gene for not-blue eggs (so if their mother did not have the blue egg gene either, they cannot lay blue or green eggs.)
If the rooster has no copy of the blue egg gene, then he cannot give it to his chicks either.
Depending on the hatchery breeding program, they may be sending out chicks that are pure for the blue egg gene (2 copies), or chicks with one copy (because they're doing crosses), or even no copies (if they have been doing crosses, and reached a generation that includes some chicks with no blue egg gene.)
If you want to know for sure, you can test-mate the rooster: breed him to the Silkie hens, raise some daughters until they lay eggs, check what color eggs they lay. If you get one that lays blue or green, and one that lays cream or brown, you know the rooster has one blue egg gene and one not-blue egg gene. If you get just blue/green eggs, or just cream/brown eggs, after testing some number of daughters you can be fairly sure the rooster is pure for those genes (6-12 daughters can be a reasonable number to test in those cases.)
There is now a DNA test for the blue egg gene, which is much faster than raising a bunch of daughters and looking at their egg colors. Considering the cost of raising those daughters, the test is probably cheaper as well as faster.
https://iqbirdtesting.com/blueegg