No, not at all.
What diode are you using ? you can check the datasheet for the leak current.
The 1N4007 has 5uA.
To charge a battery of 110mAh with 10% it would take 3 months. But the leak current of the battery is larger than that.
I think the voltage drop over the diode is your problem.
A li-ion battery will vary from 4.2 down to 3.0 or lower.
With a normal diode you need 3.3 (Vout) + 0.6 (0.5 or 0.6 diode voltage drop) + 160mV (LDO voltage drop) = 4.0 V
So if your battery is still almost full at 4.0 V, the circuit stops.