No, that will not give full range sound! The amplifier is low-passed at around 100 hz or so. It is a subwoofer amp. The factory speakers played a dual role of full range and providing extra bass. Hooking up the amplified wires to a speaker only gives low bass. It does not give any midrange. There is not any midrange on the amplified signal. NO MIDRANGE.
If you hook the amplified wires to a 6x9 and the other wires to a tweeter you will have deep bass out of the 6x9 and high frequencies out of the tweeter. There will be no midrange! No guitars, no voices, no snare drum. It will sound like crap.
I have my speakers hooked up with only the amplified signal. There is only bass coming from my rear deck. Just like if there were only a subwoofer back there. There is NO midrange. Only bass. Deep bass. It is not some muddy sounding mix of bass and mid.
I'm sorry for repeating myself so many times, but I don't want anyone to get confused and ruin a set of speakers or just otherwise be disappointed.
To clarify some more...
1 set of wires provides amplified bass-only signal. Those wires are hooked up to one voice-coil on the 6x9.
The other set of wires is a low-power, full range signal. It is hooked up to the OTHER voice-coil on the 6x9 AND the tweeter. Just like a regular co-axial speaker.
The factory 6x9 has dual voice coils on the 6x9. The wires do not power only the 6x9 and only the tweeter. One set powers the 6x9, the other set powers the 6x9 AND the tweeter.
The wires that power the 6x9 AND the tweeter are not amplified by the factory amplifier. Those wire simply pass through the amplifier and are only powered by the factory head unit.
If you want full-range, powerful sound from a replacement set of 6x9s, you will have to add an amplifier and use the signal from the full-range wires as the amplifier's input. That's the only way I can see to do it.