Yes, this system will work fine...
If your goal is to add a screen and a DVD player, you don't really need anything else unless you want something extra. I would use the internal features of the Pioneer system, but still use the factory amp and speakers, if you are pleased with the sound of your factory system. The amp and speakers are matched pretty good, and will sound fine. Although, if you are spending bucks like this, you might as well take full capacity of the compnents and build an aftermarket syatem around it...You might need some adaptors to Bose/Pioneer comonents, so make sure to ask the person doing the install beforehand...