Not exactly. The current drain of 40 mils will kill the battery much faster than the rated capacity. A 200 mil battery has a maximum drain rating of 15 mA/H. Over this, and the battery projected run time( and chemistry) is severly affected. A one second burn is actually a pretty long time for these critters. Using a sizeable cap will help, but size will probably be at a premium. Reducing on time is the best way to stay within specs.Look at a couple of months for a reliable estimate.

Ron