quick NMOS answer: No. You have a body diode that opposes conventional current flow. You put a negative voltage on the drain (with respect to the source) and the body diode will conduct. The drain will sit at -0.6V. To get a true switch, you need back to back PCH FETs, like on page 1 of this datasheet: https://cds.linear.com/docs/Datasheet/4365f.pdf
This will close off the channel going from left to right and right to left