No... The "rumor" is that a 9V battery doesn't last long enough for anything useful, so a coin cell (or two) isn't going to have any useful life, if it works at all... (I've never tried running an Arduino off a battery, except for a car battery, and I've never made the calculations.)
You may be able to "sleep" the Arduino depending on what you're doing and/or you can build a simpler version of the Arduino (with fewer components on the board) to get more battery life. I don't know anything about the shields you're using.
If you don't have one already, I'd suggest you get a multimeter and measure the current (with and without with shields). That will give you a starting-point for calculating battery life (from the battery's mA-hr rating) and you'll know where the current is "going" if you want to work-on reducing the current.