No, not like you can with a long-wave radio, the broadcast range is much more local.
For more information see <
http://en.wikipedia.org/wiki/Digital_radio >
You can, however, listen to digital broadcasts from all over the world through your computer and check out the new range of PURE DAB radios. Of course you'll see information regarding DAB+ broadcasts which are not compatible with the current DAB sets. This will upset a few million people who have already invested in their DAB sets.
Nothing changes!