Always on lifepo4 power supply - will this circuit work?
There are two considerations with using these cells. One is keeping the cells in balance after repeated charges. The other is safety if the cell ever gets charged over voltage, shorted out, or whatever. (With LiFePo4 you are already on much better ground than with for instance LiPo, even so this has to be considered.)

You can buy cells with or without internal protection (basically a tiny PCB that goes open the moment bad things happen) and if you you get them with, that is already one major consideration less. In the RC world they typically buy these cells as a pack, and then they are charged together in bulk, with chargers that balance the cells during the charge process. Basically if one cell charges faster than the others, a transistor across it bleeds off current until the others catch up. There is no real alternative, as all cells get the same series current.

However, if you buy individual cells instead of a pack, and charge them individually, the whole problem is much simplified. Cells are kept in balance automatically, and if one ages faster than the rest you don't have to replace the whole pack. Also it is much easier for a single cell charger to ensure that its cell is never exposed to overvoltage. You pay a bit more up front for battery holders, chargers and so on, but there is less to go wrong.

Regarding the powering arrangement - I would do the diodes the other way around -  a classic "diode or" arrangement: 







simulate this circuit &ndash; Schematic created using CircuitLab

This so that everything has a common and unambiguous ground. Or - as you presumably know when you are plugged in - why not a chunky SPCO switch? then no diode losses or leakage at all.