I disagree. The meter will draw about 1mA when everything is working fine, but when part of the wire chafes through and touches a ground, the current through the meter makes no difference - you're going to draw current through the wire until it burns. This is why you do need a fuse in the circuit - it has nothing to do with the meter and everything to do with the fact that you have a wire connected to a battery.Correct. A wire that is 22 AWG is rated for 1.84 AMPS. The rule of thumb is take the maximum load of the wire and multiply it by 1.5 to determine the fuse size: 1.84 X 1.5 = 2.76 AMPS (fuse size) Which is absurd for a wire that is drawing a maximum of 1 milliamp. Worse, since you are trying to monitor a critical voltage, it is imperative that you have minimum resistance loss to get an accurate reading. Adding unnecessary fuses inline, and the potential for corrosion would just hinder the voltmeter from accurately measuring the voltage. A an ex-electronics technician, I have never seen a fuse in-line with a meter. Ever.
As for any potential voltage drop- since the meter only draws 1mA, you'd need to have a 100 ohm resistor to see a 0.1 volt drop in voltage. Since fuse resistance is measured in milliohms, you're going to see a voltage drop of less than 0.001 volts - way less than the resolution of the OP's meter.