In order to have a separate amplifier you have to have those door speakers wired to the actual amp.
Yes hooking a separate amp to your door speakers makes a world of difference in quality of sound and SPL (loudness).
What happens when you run too much bass boost, full volume, improper equalizer settings, etc etc. The audio signal wave, which is supposed to look like a heart line (Peak to Peak), will start to clip (bad) which is that signal flat linning at the top and bottom of the waves. Otherwise known as distortion.
In order to get the best sound out of your door speakers, amp or not, do not turn your radio up more than 2/3 - 4/5 the volumes max. For instance on my kenwood it can go to 36, I won't take it past 28-30 depending on the quality of the song.
The easiest way to put an amp through those door speakers not going the traditional run all new separate wiring for the door speakers. (PITA door jams lots of trim panels and door panels have to come off) You could take your head unit out and disconnect the speaker wires that are coming off that after market harness and splice and run those to your amp...
I would recommend if you go that route to place the amp either under the drivers seat,under rear seat, or behind the rear seat. Great amplifier brands are Sundown, PPI, USAmps, Audison, Rockford, etc. they all make great 2 and 4 channel amplifiers. With your setup i would recommend a 2 channel class A/B amplifier. The specs would be, 2x(150-250) watts @ 4ohms.
if you have any other questions lmk