Yes, you need that tunnel up. Read this to understand why:
https://docs.vmware.com/en/VMware-NSX/4.1/administration/GUID-0E28AC86-9A87-47D4-BE25-5E425DAF7585.h...
Often the tunnel is down if you have MTU mismatch between the TEP VLANs. You need at least 1600 bytes MTU between them, depending on your configuration. If you have different VLAN IDs for Edge TEP and Host TEP they need to be routed externally. If you use the same VLAN ID other requirements apply.
