Yes, if the Join Request was accepted. So: if the packet was not somehow mangled, which would make the MIC fail, and if the node is configured with the correct DevEUI, AppEUI and AppKey and used a unique DevNonce for LoRaWAN 1.0.x.
If multiple gateways received the Join Request (orange icon, possibly not shown in the gateway’s Traffic page, but surely shown in the application/device’s Data page, if accepted), then only one of those gateways will show the Join Accept (green icon) in TTN Console.
Clicking an item to expand it, should show much more! Make sure there is no error, such as OTAA shows "Activation DevNonce not valid: already used" or Activation not valid - no gateways available.