If ChaCha20 is being used just as a CSPRNG, is nonce needed?
No it doesn't matter, as you won't be switching the nonce on a per message basis, just outputting a stream of random data.
However, remember, your key will only produce an output stream valid until the internal counter overflows.
Consider XChaCha20.
IETF ChaCha20 uses a 96-bit nonce and 32-bit counter, XChaCha20 uses a 192-bit nonce and 64-bit counter. The 64-bit counter lets it encrypt 1 Zettabyte of data, i.e. output a large random dataset.