Undetectability is hard (impossible?) to establish outside of thought experiments. Real examples are limited to undetected and apparently-unlikely-to-be-detected phenomenon. But if I took your question charitably, I would personally say absolutely yes. I've always been fond of stealing Maxwell's example: if there was a system of ropes hanging from a belfry, which was itself impossible to peer inside, but which produced some measurable relation between the position and tension between all the ropes, then what can be said to "exist" in that belfry is nothing more or less than that relationship, in whatever expression you choose (including mechanically, with imaginary gears or flywheels or fluids or whatever). And if later we can suddenly open it up and find that there were some components that had no effect on the bell pull system (for example, a trilobite fossil with a footprint on it), then I would have no personal issue with saying that those components did not exist back "when it was impossible to open the belfry." But I hold this out of convenience, not rigor.