Nope, not with Zero Lipo I don't think.
LiPo charging is a dangerous game, and hence the Pimoroni people didn't include this in the Zero Lipo (explained in a past episode of the Bilge Tank on Youtube).
If you want that kind of functionality, the best thing would be to use an Adafruit Powerboost 500C or 1000C. These have the whole charge/power at once thing you are looking for. You can even not solder in the USB connection and run the + and GND lines direct to GPIO pins. Just be sure that they're the right pins....
I believe that they said that they may consider a future 'advanced' edition of the Zero Lipo with charging though.
I am currently working on a solution with a LiPo charger and Zero Lipo to do roughly what you say, so I'll post here when I've done it.