Short answer: No.

Long answer: Typical projectors have two lenses. The one at the front is obvious, since it focusses the image of the LCD/film onto the wall. Just behind the LCD/film is a collimating lens (usually a Fresnel lens), which ensures that all the light produced by the lamp is focussed so that it passes through the first lens. Something like this:

           |Collimating lens
           ||LCD
  Lamp   .-||-.      |Main lens
  |   .-'  ||  '-.   |   .-'
  |.-'     ||     '-.|.-'
  O--------||--------|------
   '-.     ||     .-'|'-.
      '-.  ||  .-'       '-.
         '-||-'

The light brightness over the plane of the LCD/film must be very even, and this is achieved by having a lamp situated a fair distance behind it. The lamp itself must therefore be small in order for its focussed rays to fit through the aperture of the main lens. In fact, the lamp must be (usually) no larger than the aperture in the main lens.

It is conceivable that you could arrange an array of LEDs behind the LCD, but you would have to arrange that all their rays are focussed through the main lens. The prevents us from using a large array of LEDs in the same arrangement as above, as the light from the LEDs at the edge of the array would not pass through the main lens. An alternative would be to place the LEDs closer to the LCD, and give each LED a lens sufficient to focus its rays through the main lens. Something like this:

       O.|LCD
  LEDs   |-.      |Main lens
  with   |  '-.   |   .-'
  lenses |     '-.|.-'
       O-|--------|------
         |     .-'|'-.
         |  .-'       '-.
         |-'
       O'|

In this case, each section of the LCD would be lit by a different LED, so you would have to be very careful to keep the lighting brightness and colour even. LEDs vary in colour and brightness naturally.