Well, you can, but we're looking at a charge that is comparable with the self discharge rate. I would not expect more than a quarter charge in the cells no matter how long they were charged at this rate. I think maybe 10 mA would be about right.
To select a series resistor, you have to consider the DIFFERENCE between the charging voltage and the battery voltage, and the voltage drop across the diode. I fear your example would give no measurable current!
Analog is not my strong point, I would assume as the voltage drops on the battery below 5v the small trickle current would simply keep them topped off. The sleep current is only a few na, I can omit the diode if the scheme proves useless.
I recall the iButton Lock had a quick charge mode if the battery was dead. You would hook a 6v battery across the ibutton reader for a few seconds.