No, the Zumo 32U4 is not designed to accommodate the necessary headers to mount Arduino shields. If you want to add external hardware, you will have to make your own connections, and you will have to pick and choose which features you want to replace on the Zumo 32U4 . We give tips for how the Zumo 32U4 can be expanded with additional electronics under the "Adding electronics" section of the Zumo 32U4's user's guide, which can be found under the "Resources" tab of any Zumo 32U4 product page.
You might consider using our Zumo Robot for Arduino, which includes a Zumo Shield that is designed for a standard Arduino board (like an Uno) to plug into it, but it might be possible for you to add some shields between the Arduino and the Zumo Shield (adding extra stackable headers might be necessary to get enough clearance). As with the Zumo 32U4, you would need to check for pin assignment conflicts to make sure the pins used by your shields are not also used by the Zumo robot.