Shiverpeaks to Draknors.

Is it possible to go south from the shiverpeaks and run to draknors?

Yes it's possible if you hit Lornars Pass from Beacons Perch. And the best of luck to you

Everything from about 20 ft south of beacon's perch to droknar's is designed for a group of 8 lv 20 ascended characters. You can only form a group of 6 in beacons perch (or anywhere else in the vacinity) and if one of those is a lowbie trying to get to droknar's, you'll have at best 5 out of 8. It can be done, but it's not easy.