Yes, but also no. It's a less convenient flow, and indexing and such would be trickier than either centralized or on device, since you'd need to encrypt and distribute the index as well (or do homomorphic encryption, but I don't think it's ready for the limelight.)

I think most people are probably fine with the tradeoff between convenience and features that centralization offers, so unfortunately people that aren't are stuck with more niche products (or Apple, I suppose, although I don't think i-cloud is end to end encrypted?). I say they're stuck with niche products because I don't think it makes sense to try and offer a slider between convenience and privacy in one product, since the interface and feature sets would be so different.