No, it's not true.  The battery will wear each time it is discharged and recharged.  If you leave the 3DS in sleep mode every night, but NOT on the charging cradle, the battery will deplete and need to be recharged.  This will reduce the lifetime of the battery.

However, if you leave the 3DS in sleep mode but on the charging cradle, it will draw its energy from the charging cradle instead of the battery.

If you put the 3DS on its charging cradle every night (in sleep mode) the only time you will put stress on the battery is when you are actually playing it.

MARIO2804  wrote:

 

I heard something like this........ I beleive it is true!

You believe what is true?  That leaving the 3DS on (in sleep mode) but on the charger reduces battery life?  Do you have a source?