Yes, they do, but in order to fully charge a 4600mAh battery, you'd have to charge it from a 9000mAh battery (basically the size battery found in emergency lighting in your workplace's hallways and bathrooms). Using those small square or round portable batteries does not fully discharge their "charge" into the recipient battery, either... they reach a saturation point, where both batteries are near equal, but the donor battery will never fully exhaust it's charge into the dead one. So, to fully charge any dead battery, you'd need to supply it with nearly 2x what it needs.
Honestly, the best thing to do is charge it the correct way via wall-charger or mobile-charger (car)... and leave the gimmicky portable charging batteries for what they do best... give you a quick boost of power to a dying cell-phone so you can make a call or two.
I've had to use my MVP 2.0 as a cell-phone booster once, and the phone drained the MVP, but only provided enough charge so I could make maybe 15-min of calls and send/receive a few texts. BTW, the cell-phone battery is basically the same mAh as my MVP, which proves the point I was trying to make about portable power-packs.