the tentative charger chip will allow not only running from "AC" but even booting the device without battery - from both Nokia system 1) and Apple system 2) USB chargers. However what's probably not working resp could cause the whole device to reboot hard is GSM transmission at the higher power levels (adjusted by BTS according to roughly your distance from BTS). Since the modem can use up to several Ampere bursts of current, it will need a buffer battery or at least TX will fail. The CPU *should* 'survive' such short brownout of power supply, but I cannot guarantee that yet. Buzzword hotswap which is based on such CPU buffering during short brownouts.
Internal uSD in parallel to the existing uSD and to the planned eMMC is hardly feasible, we would need to multiplex that, and also the assumtion of it "needing almost no space" is not exactly correct. Also theoretically eMMC is twice as fast as uSD, thanks to doubled data bus width.
On the bright side, eMMC should have a rather long life span, and it's not the most complicated part to replace, actually swapping that chip is one of the simpler tasks.

1) D+/D- short
2) resistor voltage-dividers on borth D+ and D-