Can I use LC 16340 batteries to power a Raspberry PI 3 B
As long as you have a boost coverter as pictured on your e-bay link, any Li-Ion cell will be able to power your Pi3 device. The difference will be only how long the particular battery will last. 

If you use a normal 18650 size of cell, with typical capacity of 2500 mAh, (about 3.6*2.5= 9 watt-hours of stored energy), your Pi-3 will last about 10 hrs (typical web-browsing consumption of Pi3 is about 200 mA). 

If you use a much smaller 16430 (4/5 AA size battery), it has typical capacity of 400-600 mAh, or about 20% of 18650 cell, so the Pi3 will last proportionally less time, maybe 2 hours. 


  NOTE: you can't possibly get 2500 mAh out of 500 mAh battery. But you
  might be able to get 2.5 A of current from it, or even much more. But
  for a short period of time only.


Out of curiosity, you can try a tiny 130-mAh Li-Ion battery used for small quadcopters. The circuit booster still should work, but the battery will last probably less than 30 minutes.

Correction: 16430 is of CR123 size, it has about 1/2 volume of 18650 cell, and therefore it can have maximum 1200 mAh with contemporary technology (year 2017), typically less than that.