The Factory Restore USB will work on another drive. I carried out this procedure with media created from the latest version of Dell Backup and Recovery on my Inspiron 13 7347 and demonstrated the creation of media and installation onto a new SSD: [URL] Since you are using an Alienware use Alienware Respawn. Alienware Respawn is very similar to Dell Backup and Recovery.
I'm getting a 2015 Alienware 15 which does not come with a CD drive. I will be installing a new hard drive (m.2 SSD 2280) so the question is how to install WIndows 7. While Microsoft offers a OS IOS download for WIndows 8 that you can put onto a USB drive (with dell I think it automatically pulls the OS product key off the motherboard?) this IOS download is not offered for Windows 7.  So the question is will the OS Recovery USB offered by dell allow me to do a fresh install of Windows 7 onto a new hard drive in the same laptop the OS Recovery USB came with. My last resort is to buy a new copy of windows 7 and a USB external CD/DVD drive.   TLDR: Will OS Recovery USB offered by dell install Windows 7 onto a new hard drive.
Windows 7 install on new hard drive with OS Recovery USB?