Yes, if the configuration of device and TTN match, then you should see an Activation (orange icon) in the application and device’s Data page, if you have that open at the time the Join Request is received. And even if not open, you should see a DevAddr on the device’s Overview page after an accepted Join Request.
From the screenshots, it seems the AppEUI and DevEUI are correct. You can use the online decoder with the AppKey to see if the AppKey is correct too (leave the field for NwkSKey empty); probably not. You may want to reverse the bytes in the key (say, from 01 02 03 ... 15 16 to 16 15 ... 03 02 01) to see if that helps in that online decoder. And if not, use some of the other values that the supplier gave you? It would not be the first time a supplier messed up the keys: