Perfectly.
Burnham is Spock's adopted sister. That's a core part of her character. So it's perfectly logical for Spock, Sarek, Amanda and some of Spock's crewmates to occasionally overlap with her life.
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This is just my personal rule of thumb, but I'm obviously not alone with it:
If you have to recast the part, you're doing it for the fan-wank. If you're actually continuing the actor/character story, then it's okay.
I would have been fine with a "surprise" sibling of Spock twenty years ago, when Leonard Nimoy was still alive and would have appeared in cameos as Spock. 20 years later though? They're doing it entirely banking on name recognition alone. From a story perspective, she could have been the sibling of any other Vulcan, or Tuvok's father for all intents and purposes.
The same standard still applies for all eras: If suddenly a sibling or the parents of Pike appear? That's fine! Because this guy's story is being told right now. But, let's say, if the Picard show would introduce a woman and tell everybody "She's Jake Sisko's wife", but then have to re-cast Jake Sisko when she mets him? - Then that would be fan-wank, because it wouldn't be logical conclusion to the original actor/character story, but rather only a vehicle to be allowed to say the word "Sisko" on screen, and hope some DS9-fans would get duped by it.