Okay, let's do a little math here with voltages.
Say your stock head unit has voltages that would drive 4 ohm speakers to power levels of 15 watts RMS (and current capability / power supply to do so). P=V^2 / R, so 15 = V^2/4, so V^2 = 60, so V~=7.75v. Per the spec sheet of the DQL8, the max output voltage is 7.5v. So it can drive the output to about the same level as a head unit capable of 14-15WRMS @ 4 ohms. So yes, it is capable of this.
Just keep in mind that, as others have mentioned, your stock system may already have EQ in it. You can add your own EQ in with the DQL8 to cancel it out, but it can be hard to figure out what exactly to enter in order to do that. You may need a measurement system to do that. But if you just want to EQ in relation to what you already have, the DQL8 looks like one possible solution.