In the past I had troubles with Crucial M4 SSDs in the larger 500GB sizes on the Seagate Thunderbolt Adapter. This was probably due to the very large power spices this SSD produces while operating which are not present with hard disks which was what this adapter was designed for. Seagate never sold this adapter with SSDs.
However, those older technology SSDs, while power hungry, did have exceptional performance specs. More modern drives that you get today are cheaper, somewhat slower, but have greatly reduced power requirements. I have several Samsung 840 EVO SSDs running from Seagate TB Adapters with no problems.
I think you will be fine with a 850 EVO 500GB SSD on the Seagate Adapter.