The example you link to (letsmakerobots) uses the VirtualWire library and this would require the receiving side to also use this library. In this configuration a direct link to a PC USB/TTL adapater would not work.
As an alternative you could connect the RF transmitter to the Arduino USART and then use Hardware serial (Print statements) to send data via RF directly to a USB/TTL connected RF receiver. The downside to this is a less robust protocol (VirtualWire implements some clever error/recovery schemes although at the expense of processing capacity).
Another alternative is to use an Arduino as a USB/TTL adapter which would allow you to run VirtualWire on both sides of the link.