Question about mac to mac transfer on migration assistant

I have a thunderbolt cable to do a 'mac to mac' transfer using migration assistant from the old to the new mac, my question is whether it is possible to connect an external hard drive to the old mac as the 'source' that is being transferred from.
Essentially what I want to do is do a mac to mac transfer with a thunderbolt cable, but use an external hard drive as the source on the old mac, rather than the internal hard drive.
I know it sounds weird. Long story short. I have a usb 3 external hard drive. The old mac is capable of usb 3, the new one isn't, but both have thunderbolt. The old mac has usb 2, which is too slow for large transfers. That is why I am hoping connecting an external hard drive to the old mac and using a thunderbolt between the macs for the transfer is possible.

 

The idea is that because the new computer only have usb 2 compatibility, it would be faster if it was possible to do a thunderbolt connection between the computers, with the external hard drive connected to the USB 3 compatible old computer and use the thunderbolt between the 2 machines for faster transfer.
In theory, it would be fastest way to transfer 1.5TB of content, but I don't know if it actually works.