I experimented with this setup on a short labor day overnight trip in Harriman State Park from the Elk Pen parking lot @ NY-17 along the Appalachian Trail to spend the night at West Mountain Shelter overlooking the Hudson River. The day was very sunny, but the trail was nearly constantly covered in shade. Our lunch / rehydration spot was modestly sunny, but I was lazy about putting keeping the panels in the sun.
I tested this by starting with the backup battery at zero charge. I tested the resulting charge by powering my phone off, and recording the phone charge state before charging and after charging overnight.
After 7.5 hrs of heavy shade hiking (some of that did have direct sun), my phone only gained 42 mAh of charge overnight! That's 5.6 mAh/hr in shade.
Caveats: this does not account for the phone battery power consumed in shutdown and startup, and the solar battery might charge my phone less efficiently when it's near-zero charge?
In the next few days, I'll repeat this experiment hanging the panels out my apartment window to see what the maximum charge comes out to.
Droid Incredible 2
Airplane Mode on 95% of the time (turned off briefly to check Google Maps for an AT hiker, and at the end of the hike to text family)
Backcountry Navigator checked several times for GPS/map guidance
Backcountry Navigator set to track @ 1min interval, 20m min distance, 300m gps accuracy
This "heavy" use consumed 535 mAh over 7.5hr; 71 mAh/hr
On the return trip, I used no BC Navigator tracking, but still used it for guidance. (I'm not certain, but I think BC Navigator my keep the GPS on constantly unless you tell it to turn off the GPS... I might have been able to save more power)
This "light" use consumed about 45 mAh/hr
Clearly there is still a bit of a gulf between what the phone consumes and what the panels produce... thankfully the 6000mAh battery will store 10+ days of 12hr "light" use... so that's good.