No!
Metal detector use or have within them a voltage regulator. The regulator regulates the voltage down to a point lower than the MAX output of the batteries.
(For Example)
A detector that uses 12volts will likely run at 8 volts. So it would have a ceiling or a reserve of 4 volts to use before a low battery problem would happen.
A detector that uses 9volts for its power supply will be regulated down to somewhere around 5volts, giving it a 4volt ceiling as well.
Now one running on two 9volts is most likely still actually running at 5volts, not 18volts, in this case the batteries are "paralleled" to double reserve current and to help with extended run time. Some of these units will in fact run with only one battery in them (some of them)
So, what would happen if you took a 9volt unit and supplied it with 12volts, would you gain any performance? "NO" the reason is because the built-in regulator is still going to cut it back to 5volts, if it can handle that much over voltage! it could burn the regulator up even trying it!
Now, without a regulator you would have one quirky detector, it would work more like a light bulb, starting out Bright and minute by minute getting a little dimer (weaker and audio loss)
Why do the designers use diffeentr voltage supplies? There is a lot of reason for this. I do know that as more and more micro electronics are being used its taking less voltage and current to drive them.
Mark