It would work, but with much reduced speed. Converting SATA to TB (which happens inside the HDD case as all Hard drives are made with SATA outputs) doesn't inherently slow things down, but add what is essentially a certain % SATA communication data to the stream that the TB sends (which has its own communication data) this then gets added to the USB 3.0 stream. It's like russian dolls, a box in a box in a box giving you less space in the box for your actual HD data to travel in. Your SATA to TB to USB then USB to PCI-E then PCI-E to SATA software adapter would thenopen all the boxes but the speeds you would get would be much less than half the 5Gbps rated by your weakest link (USB3 in this case due to polling).
Finally, USB and TB work in fundamentally different ways, one is asychronous peer to peer (TB) and the other is master slave polling (USB3) this massively hits TB speed out of the box as the data stream in essentially "quantized" (held back until the next tick of the USB clock). In short, your speed loss doing this would make your connection closer to FW800 league than true TB.
eSATA, on the other hand is a direct, no conversion connection at all. eSATA *is* SATA just with added electricity and a clicky plug and that's what your drive takes.
So in short, it would work but it would be a supreme waste of money and power if you have an eSATA option available to you. I strongly suggest you reconsider your decision.