Not automatically but it's pretty easy to do with the VirtualGPS if you're a paid member.
Create a VirtualGPS at https://project-gc.com/User/VirtualGPS
Go to the map you want, if you want all challenges you have qualified for I assume https://project-gc.com/Tools/Challenges?map
and remembering to exclude "not fulfilled" and archived.
Optional: Remove the ones you've found by clicking the GX-logo and then the smiley-icon.
Click the GPS-icon and choose the polygon-tool, draw around all the caches you want, click the GPS-icon and click the one GPS-icon with a green plus sign. Now all the caches that where inside your polygon is in your VirtualGPS.
Go back to https://project-gc.com/User/VirtualGPS
and choose export as GPX or select what bookmark list you want the caches placed in (needs to exist on Geocaching.com so you need to make a new one if you want a bookmarklist with only the caches from the VirtualGPS).