I would expect a small amount of drain. probably not enought to worry about. I think for someone to answer this better we need to know what type of volt meter you have. There are several different methods used for measurements.
Why not put a momentary push button on it. Push the button to see what you have and then let go. Anything electrical draws power. How much depends on the meter but it is simply silly to leave a voltmeter powered 100% of the time.
Here is a better idea. Put a cigarette lighter type power recepticle at your helm. You can use the in dash type or the under dash type. Now buy a digital voltmeter from Wally world. If you want to use a spotlight or battery charger, just pull out the voltmeter and plug it in.
The digital voltmeter draws such little voltage, it would take years of use to draw down your battery.
John
Don't forget to add a 20 amp fuse in the line to the recepticle. You can also run an inverter if you have need for one.
John