Does a switch schematic symbol have a conventional "polarity"?
No a switch doesn't normally have polarity, but when you implement a switch with semiconductors you have to worry whether they are one-quadrant, two-quadrant or four-quadrant, depending on what the rest of your circuit requires/imposes in terms of current and voltage. For example a BJT is good a 1st quadrant (or 3rd quadrant) switch and a diode as a 2nd quadrant (or 4th quadrant) switch. A MOSFET is good as two-quadrant switch if well chosen (body diode considerations). A good presentation of that topic is in Erickson's course.