no, it will not, the books need to be downloaded wirelessly from the website from your account. This is where information to sync the two devices is stored. Also, if those books were originally downloaded to the original Paperwhite and then copied (sideloaded) to the second Paperwhite, most of them will not open because they are DRM protexted at the moment they are downloaded to only open on the device to which they were downloaded.
what I meant is that the only ways progress on two different devices is synced is either manually (you'll need to remember where you are on one device and page forward on the othe one) or the books are stored on your account (not your computer/external hard drive/Cd/DVD/etc) having been sent to your devices through one of the following methods:
then when you turn on wireless and sync (menu option or icon) a device to the account it will store the current reading location and when you do the same on another device, it will see the latest page you've read. Kindles do not sync to each other, they sync to your Amazon account