I haven't used battery-case combinations like the link you provided, but I have used cheap USB chargers like this: http://www.amazon.com/Duracell-Instant-Charger-Includes-Universal/dp/B002FU6KF2
... it's just like plugging into the wall or your computer so you can still use the phone while it is charging. I can't say exactly, but one of those USB chargers would probably charge your phone up once.
Another tip is to put your phone in Airplane mode. The battery will last a LONG time that way. When you want to check your progress, take it out of airplane mode and let it sync. I'm assuming the re-sync/connect progress would be quick.