Switch off branch of a circuit when voltage is present in another branch [power path management]
I see an issue with your circuit, the charging current of the battery isn't (properly) limited in any way.

As it is now, suppose VCC would supply 6.8 V at very high current, the battery has very little charge and is at 5.5 V for example. Then there would be 1.3 V across D1 and that could be an issue. Too much current could flow potentially causing damage to the VCC supply, the diode and the battery. That's not good.

We EEs generally like to avoid such scenarios so we invent solutions to avoid it. The solution is simple, add a resistor!

How about this schematic:



I got it from this article which uses 2 AA cells but that doesn't matter. The working principles still apply all the same.

The 1 kohm charging resistor will be too high value for your situation, you will have to recalculate it. You will probably end up with something like 2.2 Ohms or so (just my guess!!). Make sure that the resistor can handle the power it will dissipate at the highest charging current (when the battery voltage is low).
For the diodes use a type which can handle the current. Schottky diodes can be a good choice but ordinary diodes will work as well as long as you account for the slightly higher voltage drop.