Yes, just confirmed it can work without battery.
The charging circuit pumps 4.2V. I added a 470uF cap just for safe of mind.
Unfortunately I baked two of the circuits by undoldering the CS5460A and one of the memory eproms 24C02. Eprom I have around, easy fix. The chips need to get some from Aliexpress.
I was trying to remove them to clear underneath as there was some green stuff in the pins.
Seems hot air station and memory chips and some this specific power measuring chip dont go along.
I did the same mistake in two so the other are fine. Firts I thought something else was wrong and moved on to try to have a comparative system which I could measure to come back to the first but at second failure I imagined I was the issue and reviewed what I was doing wrong. I think I would have to unsolder by leading the pins first and hot hair undernead afterwards or maybe get some low melting point stuff.
Anyway, always learning something.