Is there any reason to leave the battery in my spare remote, which will probably sit in a drawer for years? Taking the battery out will ensure that the remote will work when needed without a quick trip to Radio Shack. Unless, of course, it does just the opposite?
That would work. The battery has a shelf life of about 11 years. Unless of course, you broke it removing or replacing the battery.
You may want to consider removing the battery and storing it inside the vehicle somewhere. What I've found is that you can tie-wrap the keylet to an undisclosed exterior location, and store the remote sans battery inside the car, hidden deeply. That way....if you lose your primary fob/key when you're far from home, your car does not become a 3500# paperweight until you go and get the second fob. Lotsa different ways to do it, but to answer your question: Yes. You can increase the life of the fob battery by removing it. Worth doing? YMMV.