No, the TA-nmon does not require any specific privileges.
The scripts should be executable by the Unix user owning the files, and running the UF. (which is the case by default with the TA will be deployed)
The performance collection itself (driven by the Nmon binaries) can be perfectly run on any non privileged Unix account.
Note that you will go into trouble if you try using a Windows based to deploy the TA to Unix clients. (because Windows will not preserve the Unix permissions.)