Mature Sculptor brains and nervous systems are mostly Other, any memories and habits they retain being stored on the new upgraded hardware. The rest of their bodies are mostly natural, but their genes are heavily altered, and probably contain Gap matter in the rewired DNA. Even with both factors considered, the total mass of a Sculptor that's unnatural is a fairly low proportion. So no, I don't think White Giants will harass Sculptors, though the two will probably put each other on edge.
But White Giants will almost always seek out and destroy the Sculpture they use to reproduce, and that brings the two into conflict. The artwork is abandoned once it is finished and the polyp has nestled in, but before then, or during a performance, like a song, the Sculptor is actively involved in producing an Other creature and will be targeted unless it flees, which it will only do reluctantly. If it thinks it can disable an attacking White Giant without it or its art being destroyed by the final detonation, it will do so, and its intelligence helps it even up a lopsided fight. Moreover, once it learns that all White Giants behave identically, the Sculptor could try to pre-emptively trap or destroy those in its current territory to secure its future projects.
tl;dr The Sculptor's safe but the art isn't, and Sculptors don't like being interrupted, so it's entirely possible that we might see some fabulous duels between the two.
Should've cleared this up earlier, whoopsidaisies. Also, I'm including a bit of Ant Hero in my next post.