I'm trying to put this a nice way - so apologies if it comes across harsh.
The accelerator pedal, is connected to the throttle body via a cable. Basically, you push down on the throttle, it pulls the cable, opens the throttle body. This lets the air into the engine. The further you push your foot down, the further open the throttle body gets.
The TPS sensor tells the ECU (engine management) how far open your throttle is, and adjusts fuelling/ignition/etc to suit. So if the throttle is only partially open, the ECU will fuel to suit a nice cruise, and will not chuck in loads of fuel etc. If the throttle is fully open, it'll act like you're accelerating hard, and put in loads of fuel.
So in short..... yes - a TPS sensor is definately needed.
What you're ECU will be doing currently - with the sensor unplugged - is taking its best guess at what is happening from other sensors. To be honest i'm surprised it runs/idles at all without the TPS. From the other sensors it'll know roughly what is happening with the throttle body by guessing, and roughly do what it guess to be about right. Notice the amount of 'roughlys' and 'guesses'.
You've probably got one of two issues.
The first is that you've got a dodgy TPS sensor.
The second (which i'm putting my money on) is the fact you've gone for a rallye inlet but probably - i'm guessing - stuck with the standard ECU and not even had it remapped to suit.
When you open the throttle, it sends a signal to the ECU.
Take for example;
VTR Throttle - Fully closed sends a signal of '10', it slowly rises until fully open at '30'
Rallye Throttle - Fully closed sends a signal of '14', it slowly rises until fully open at '34'
What has happened is that the ECU will be programmed to know what to do with a throttle signal of anywhere between 8 and 32. But you're now trying to send a signal of 34 to it, and it hasn't a clue what to do. When you unplug the TPS sensor - it still hasn't got a clue what to do with a '34' signal, but is no longer getting it, and guessing what to do from the signals from the other sensors.
Options;
1) Refit standard inlet/throttle body
2) Leave rallye inlet on, unplug TPS. Notice fuel consumption maybe increases a lot, and potential damage to other sensors/engin itself due to over/underfuelling.
3) Remap or get standalone, and recalibrate the ECU to the new max/min throttle signal.
