Since aqueous acids release Hydrogen cations into the solution, will an electric current create Hydrogen gas?
Yes.  In fact the first electrolysis was done with acidified water.  Pure water is only slightly ionized and is a poor conductor.  Adding ions to water increases its conductivity and speeds up the electrolysis process.  So by adding a source of protons to pure water the following reaction will occur at the cathode $$\ce{2H+ (aq) + 2e^{-}-&gt;H2(g)}$$  Of course a parallel reaction will occur at the anode $$\ce{4OH- -&gt;2H2O + O2(g) + 4e-}$$ otherwise a current wouldn't flow and the electrolysis would not continue.