Is mechanically switching SATA drive signals possible?
With a mechanical switch or relay? No, that will absolutely not work.



Here's what a SATA cable looks like internally. The shiny bare wires at the top and bottom, and in the middle, are drain (ground) wires; the copper wires in between those are what carry the signal. As you can see in the picture, they're embedded in a dielectric material. This is to maintain a consistent impedance, which is critical for signal integrity at 6 Gbit/sec.

Bringing those signal wires out of the cable to a mechanical switch will ruin the electrical properties of the connection, and is likely to either prevent the drive from being identified at all, or cause a large number of link errors. If you need to switch a SATA signal, you will need to use an IC specifically designed for this task.