Will Active Partition Recovery for Windows restore a USB flash drive (i.e. Memory Stick) that has been low level formatted (i.e. formatted to prevent data from being recovered) and as a result is no longer useable (cannot be formatted or written to)?

No. File recovery may be able to recover the data, but partition recovery can not help if a drive has been formatted. (Sometimes it can help if the drive was FAT32 and formatted NTFS and vice versa, but it can not help if the disk has been formatted, quick or full, using the same file system). Partition recovery only recovers the partition information, and formatting overwrites file system info (file tables used / unused space etc).