Yesterday I decided to set my radio up on a QRP (5 watt) beacon mode on 80 meters (I used a propagation mode called WSPR, transmitting once every 10 minutes). I let the rig run from about 4:45 PM local time yesterday to 11:00 AM this morning. In that time, as you will see from the map, I was copied pretty much everywhere in the US and Europe. I also made it around the globe to Tasmania (that yellow colored line heading off the bottom left corner).
Pretty much proves that QRP can work the world, even on a band like 80 meters, not usually the #1 choice for DX.