At the beginning of the third part of Seveneves Neal Stephenson describes how the protagonist Kath Two travels from the Earth's surface into the orbit with the aid of a Skyhook-named system. The route between the earth's surface and the skyhook is laid back using a glider, which can reach without any drive only by clever exploitation of thermals up to about 100 to 200 km altitude. My question now would be, is it possible to ascend to such a height using a sail glider?
From my memory of the book there's no actual altitude listed, but the suggestion was that the glider had to reach very high. The current glider altitude record is just over 50,000ft:
The highest altitude obtained in an unpowered aircraft is 15,460 m (50,720 ft) on 30 August 2006 by Steve Fossett (pilot) and Einar Enevoldson (co-pilot) in their high performance research glider
So I would say that currently it is not possible for a glider to reach the kind of altitudes the book alluded to. Seveneyes described a society with much more advanced technology than we have now, the glider itself had the ability to morph its shape considerably, it's hard to say how high a glider like that could get. This is science fiction after all.
Project Perlan 2 aims to fly a glider up to 90 000 feet. 100 000 feet (30km) also appears possible, but more expensive — presumably due to complex composite construction to reduce weight.
Soaring that high requires specific atmospheric conditions, a standing mountain wave and the right wind conditions to prevent that wave being blocked in the troposphere. As the book is set in the future with advanced materials, presumably the glider could be a lot lighter so you could go a bit higher and maybe have a wider range of conditions in which you could get to altitude.
However the required conditions are somewhat rare, so it might not be practical for skyhook(s) as they wouldn't often align with the right weather.