Does a Mcp23s17 output pin keep the value after being unselected?
Any GPIO expander will keep the state it is set to, until it is set to a new state. It would be a pretty lousy expander if the pins changes to some other state while you access another device over the same bus.

The open drain emulation means that the IO pin can be set to push-pull output where it outputs high or low, or it can be used like an open-drain output, where it never outputs high, but can be set to output low and high impedance state.