That is correct - it should not show a voltage drop because you are connecting it effectively straight across the supply; all three are in parallel: supply, resistor, voltmeter. In parallel, all items see the same voltage, but the current through them will vary according to their properties.
Do some google research on series and parallel circuits.
Oh, and ideally, a voltmeter would have infinitely high resistance so that it does not take any current away from the circuit. 100MΩ is good. With a low resistance to the voltmeter, as you have seen, the voltmeter itself becomes part of the circuit and causes changes. That is not what you want.