Do we need another controller when using ArduPilot?
There are a few key points worth making before answering your question:


Ardupilot has undergone a re-branding and is now known as APM; this change was made to reflect that the technology has grown beyond strictly using an Arduino environment. You can see this for yourself at their website.
The term(s) Ardupilot/APM have been used somewhat interchangeably for both the hardware and software. This can be confusing so I'll refer to the hardware as an "APM Kit"


Can I simply program the ArduPilot, connect a Wireless interface to it and merrily be able to control it ?

Yes, 3DRobotics offers APM Kits that are plug-and-play hardware packages with preloaded firmware. They (optionally) supply all of the components needed to operate a small unmanned hobby aircraft including:


Power module
Transmitter and receiver for the APM-to-Ground-Station link
GPS module w/ compass


The user is generally expected to provide:


Airframe
Batteries
Servos
RC transmitter and receiver
An additional voltage-regulator/BEC if using high-torque servos
A computer (groundstation)


However, the unspoken question is:

How easy is it to setup Ardupilot/APM to work safely and correctly?

In truth, it takes considerable effort to put together a properly working system. The plug-and-play hardware saves you a great deal of trouble but tuning and operating an RC aircraft requires a different skillset. If you're experienced in RC, this may not be a problem.

From experience, you can expect to spend a number of weekends configuring and tuning APM (the software) even if you have a perfectly tuned RC aircraft.