Voltage across the IC
Your understanding is not correct. The on resistance of the switch will only drop zero voltage if you draw zero current through the switch. Ohm's law should tell you right away that the voltage drop across the switch is going to be a direct function of the switch resistance and how much current that you intend to pass through the switch. 

I get the sneaking suspicion that you are making an X-Y type query here. You have three power supplies that you need to gate to a device under test. Why don't you consider making a single power supply that has an adjustable output. There are plenty of both power management ICs (both switching types and linear types of regulators) that support adjustment of the output voltage through a feedback voltage divider. These are very easy to setup with a switch IC like you showed in your question that selects one of three separate sets of feedback resistors to set the output voltage. These resistors are usually in the 100's or 1000's of ohm sizes operating at low current such that the low RdsON for a modern type of analogue switch part will be insignificant to the application.