They can pretty much avoid any discussion of Kirk or the Enterprise until season 8 or 9. If it makes it that far.
Yes and I'm OK with that. However Sarek is a major figure in DSC with a "familial" relationship with a human Starfleet commander. Every time I see Sarek in DSC, I'll be reminded that at that moment, his son Spock is a Lt. Commander aboard the USS Enterprise. Is Sarek to act as if his own son doesn't exist? That's gonna be a tough sell.
Yes, Sarek did do just that. Sarek opposed Spock's entrance into Starfleet and the two were estranged for two decades. Given Sarek's nature, while he might have kept tabs on Spock due to his diplomatic ties, it wouldn't be logical for him to mention anything about Spock at all.