Will my chosen amp and speakers work well together?

I recently bought a 2006 honda accord. I wish to leave the factory stereo in place but I want to both improve on the bass and the clarity of the sound.

I already have a sub and amp that I have used in the past and I know they work well together, so that covers the bass. I plan to add a set of 6x9's in the back and a set of 6.5's in the doors

The components I wish to use are
Rear Speakers: Pioneer 6x9" 5 Way Car Speaker Pair TS-A6995R TSA6995R(100rms each speaker)
Rear Speaker amp: Audiobahn A4004T(50rmsx4 channel)
Door panel speaker: Pioneer TS-A1675R 6-1/2" 3-Way TS Series Coaxial Car Speakers
Door panel amp: hoping to hook straight into the head unit
Line converter Kit for subs and 6x9's: AudioControl LC2i audio converter

I have tried to the best of my understanding do the background research before posting I know that the amp needs to be 50% higher than the speaker it is powering in terms of rms watts but the audiobahn I read on the specs is capable of "200 watts RMS x 2 bridged output" so I'm hoping it should power the 6x9's

I have the same car as you. But I don't know if your car is a coupe or a sedan.

Instead of hooking up your speakers to the head unit, hook it directly to your 4 channel amp along with the 6x9's. Make sure your amp is putting out enough power to all your speakers. If you're using a crossover or anything, make sure they are set and tuned properly.

I'm assuming you have no idea how to run the speaker wires from your amp to your front speakers. If you need help with that, you can send me a message on here.

I don't know where you got that 50% thing.
The RMS rating of the speaker is the ideal amount of power the manufacturer believes should be used to power the speaker. Obviously it doesn't have to be exactly that. 10 or 20% more is perfectly reasonable, but 50% is not. And having presented it as a known fact makes me question where you've been doing your research.
At double the rated power of the speakers you will need to be very cautious in adjusting the amp (no bass boost, low gain) in order to keep the speakers happy.

All that aside --
When you go to a concert is it set up so that the sound comes from behind you?
In trying to set up a "sound quality" system in a car, it is standard procedure to focus on the front speakers as your main source of full range sound. Many high end set ups use very low power to run the rear speakers (or no rear speakers at all).
It is counter intuitive to have a bunch of power on speakers in the back of the car and minimal power on the fronts.
Another good example -- a high end home sound system (for music, not movies) -- these can easily be $5, $10k+ set ups… There ARE no rear speakers. There's left, and there's right. Same for recording studio monitors.

My experience with pioneer speakers is they don't perform very well with a lot of power from amplifiers. Just stick to 50 watts rms per speaker. You don't need the 50% more power thing. Just get an amp that does 50 watts rms at 4 ohms per channel and it will be fine. The speakers you are looking at are pioneers a series speakers which is their more affordable line of speakers, they have very strong highs, but have weaker lows. A more balanced sounding speaker would be alpines type s speakers or kicker k series speakers. A very good upgrade would be pioneer d series speakers. They probably sound best out the the speakers i mentioned but they are not the loudest. And its relatively easy to over power them.