This is going to be a lot of... hmm, I’m not precisely sure what to call it. I don’t want to say it’s just a theory, because that takes away from how much it’s evidenced in canon. But I don’t want to call it canon, because the canon isn’t 100% clear on this. So it’s somewhere in between those two things and not everyone is going to agree, which I think is helpful to keep that in mind! ♥
My answer to this question is: No. Because Chibi-Usa’s Sailor Crystal is her own, it’s not Usagi’s Sailor Crystal. In the scene where Chibi-Usa’s Silver Crystal forms, we see that there are three of them there in that scene--Usagi’s one, Neo-Queen Serenity’s one (that Minako is still holding) and then Chibi-Usa’s. Later, hers becomes the Pink Moon Crystal, when she’s not emulating her mother so much (which is why hers is initially a Silver Crystal, because she’s patterning herself after her mother/after Usagi), cementing that Chibi-Usa is her own thing.
Which assumes you mean it in the sense “could she inherit the Golden Crystal”, rather than, “Could she theoretically take Mamoru’s Golden Crystal and use it?” which she could, in the same way that the Sailor Animamates used Sailor Crystals after they murdered their holders, the same way Metallia wanted to snatch the Silver Crystal and use its power for herself, etc.
Each Sailor Crystal is the Star Seed of the person it belongs to, which seems to be like their soul and each of them is unique, so Chibi-Usa’s is her own and not anyone else’s. ♥