The question: Is this possible because the hardware makeup will be completely different on the custom built PC.
It might be possible. Generic Win7 driver support is pretty good. You'd want to proceed carefully of course.
If I was trying this I'd shrink (resize) the desktop's primary disk partition, create a 2nd bootable partition and install the laptop iso image there.
Essentially, you're creating a dual boot OS on the desktop.
I use Easeus Partition Master Home Edition
for managing my partitions.
for managing my multi-boot options.