I was wondering if it was possible to schedule a time for One to sync files as opposed to syncing every time I move a file into one of my designated folders.
Not exactly, no. Ubuntu One is not a backup service. Doing this could also result in conflicts, if you were to change the same file on another computer, and the files were not in sync already on both computers.
If you want to use Ubuntu One as a backup service, you might want to look at the Deja Dup application (Backup in System Settings). It will back up your files on a schedule, and supports storing the backup data in Ubuntu One.