Are you asking if it required to run a noodle to a sub panel that does not need one?
A noodle is only required to be run with a grounded service supply, SEC.
250.24(C) Grounded Conductor Brought to Service Equipment.
Where an ac system operating at less than 1000 volts
is grounded at any point, the grounded conductor(s) shall
be routed with the ungrounded conductors to each service
disconnecting means and shall be connected to each disconnecting
means grounded conductor(s) terminal or bus. A
main bonding jumper shall connect the grounded conductor(
s) to each service disconnecting means enclosure. The
grounded conductor(s) shall be installed in accordance with
250.24(C)(1) through (C)(4).