Wanna bet? Actually you may not with the partial tune you have and the full spool. I hope you know how and where to make adjustments in your software to make the trans properly shift. With 4.56 and no trans tune AND your knock sensors being turned off you will prolly pop the motor when it bounces off the rev limiter trying to change to third.
The last Mark I built had 3.73s and a blower. In the quarter I came within a hair of shifting to 4th so no doubt 4.56 would be well into fourth.
Now it can be done, I am not discouraging you BUT the trans needs to be programmed properly and the engine management needs control over the motor. You need your knock sensors back on. If they are getting false readings then stop modding the car and save for a rebuild.
If its not actual knock that makes them think there is knock you have bad rod bearings or bad tensioners or a broken crank keyway. Need to inspect that motor. My first blown motor poped on Gearheads dyno due to a bad keyway and me limiting the knock sensors controll too much.
In the software you should (I assume, I use SCT and it can) be able to set the knock sensors range and ammount of timing they can add or remove. After you get that down then you can play with your tip in timing and that will really make it snappy.
Anywho back to the issue at hand. Stock axles are not that strong and a spool with 4.56 on the street WILL break one of them. Prolly the passenger side. You have 4.30s already, just get a TL for the diff and call it a day. Work on power addition cause the trans will not like using 4th as a pulling gear and it will fail. Trans cooler, J-mod and proper tune will help it last longer but it will still be at risk.