Yes, reading progress will sync across your iOS devices, Android devices and your computer! Simply log in using the same account and all progress should be saved.
Even when you are reading offline, your progress is saved and will update the next time the device is connect to the internet. Offline books count toward your "total number of books read." Be sure to mark offline books as "finished" when you have completed them so that they are counted in your total. The "total number of books read" on your account dashboard will update to include books read offline once you are back online.