Low Cost RF Transmitter and Receiver setup

I would like to ask if it would be possible to control multiple devices (for the sake of simplicity, let us assume that we want to control LED's). We have a base transmitting device that transmits to several receivers as shown in the diagram below. Would it be possible to use the setup expressed below or would I have to connect multiple transmitters to achieve the target goal?

Receiver: http://www.leeselectronic.com/product_info.php?products_id=9476
Transmitter: http://www.leeselectronic.com/product_info.php?products_id=9475

To differentiate the LED's that are being turned on or off, the transmitting device will transmit a string that consists of two integers where each pair is separated by a comma. The first integer that is transmitted will indicate the destination device while the second will be an integer that determines the status of the LED (on/off). When serial activity is detected, the receiving Arduino will check to see if the first number corresponds with their designated number. If so, it will alter the status of the LED based on the transmitted signal.

Looks to me like it will work. There is a library called VirtualWire (http://www.open.com.au/mikem/arduino/). It provides message checksums so you won't be acting on garbled messages.

I used XRF Modules, sending 2 bytes, pin number & state

I just got some panStamps which are pretty neat. They have a RF chip and Arduino Pro Mini together on one small PCB.
http://www.panstamp.com/home

I like the panstamp idea. The accessories are kind of pricey tho.

If all you want to do is light up some leds or something similar
you can do this without any microcontrollers at all with a pair of these chips

They simply take a ttl input like a pushbutton, encode the pushbutton into a data stream which goes to the transmitter
and a similar chip takes the data output from the receiver and re creates the ttl level, so you could connect the leds directly
to the decoder chip.
In their most basic mode , they can transmit 4 bits of data so that would allow 16 leds to be controlled.
The chips cost around $2 each.