Does copper react with HCl when current is present?
A reaction between copper metal and hydrochloric acid would go something like this: $$\ce{Cu + 2HCl -&gt; CuCl2 + H2}$$
...which we can write as: $$\ce{Cu + 2H+ -&gt; Cu^2+ + H2}$$
If we break this up into half reactions, we get: $$\ce{Cu -&gt; 2e- + Cu} ~~~E°=-0.34~V$$ $$\ce{2H+ + 2e- -&gt; H2} ~~~E°=0.00 ~V$$
If we add the voltages together, we get the cell potential of the combined reaction is $-0.34+0.00=-0.34~V$. Since the cell potential is negative, the reaction is not spontaneous, so the reaction is not going to occur without any artificial interference ($\Delta G°=-nFE°_{cell}$).

However, if you connect a battery (galvanic cell) to this reaction, you can supply the necessary electrons for this reaction to occur (electrolytic cell). Since you are connecting a 12 V battery, there is more than enough voltage to cause this reaction to occur.