Is it required to have Cisco UCS servers to integrate Cisco Nexus 7000 devices with VMware NSX?
No it is not mandatory to use Cisco UCS servers.
Can you please elaborate further exactly about your design ?
If you can share more details it will be easy to understand.
NSX is independent of any physical hardware.
Have a look at the paper: "Deploying VMware NSX with Cisco UCS and Nexus 7000" http://www.vmware.com/content/dam/digitalmarketing/vmware/en/pdf/products/nsx/vmware-nsx-on-cisco-n7...
UCS is not mandatory for deploying NSX by integrating it with Nexus 7000. Any supported server hardware in VMware HCL should be fine.
Here is a nice article on NSX + Nexus 7K . It talks about normal Rack Mountable servers.
Going Over the Edge with your VMware NSX and Cisco Nexus
It is not mandatory to use Cisco UCS when using NSX with Cisco N7K.
Cisco N7K will be an upstream switch to forward North-South and East-West the traffic.