Shouldn't be an issue. Just ensure it's always plugged in to same port. When you get your new drive use the built in Windows Easy Transfer.
Personally I'd be tempted to take the drive out the enclosure and use it internally then if you still want new drive ghost it - most manufacturers nowadays have a free program to shift stuff from one drive to another.
Edit - Don't forget to set the BIOS to boot from USB, a basic but easy potential mistake.
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