Here is one case where battery can be drained for sure. :-) If you have the remote docked and connected via USB and you shutdown the PC followed by powering off the DS charger (power strip switched to off position), the remote can be drained of charge.

Now, for your application:

If you want to do what you suggest and and are concerned about draining, you can always open up the DS using T6 torx wrench and disconnect the ribbon cable inside the unit. There are basically 2 circuit boards. A main board and a connector board. If the ribbon cable between the 2 is not connected, I suspect that the there would be no adverse effect. However, if there is, you could always remove the connector board leaving a hole where the connector is and just sit the remote on the DS. It should rest there just fine with no issues. :-)