I just tested it, and the Fidelice RNHP definitely has a power-on transient (pop) that’s audible with headphones connected, and an odd woosh-pop sound if you power it off with them still connected.
The RNHP manual states:
We recommend powering the RNHP ON and OFF without any headphones connected. This promotes long-term, stress- free operation for the user, the RNHP and pair of headphones.
This is a bit dissapointing in a $1,195 amplifier. Even the $100 Schiit Magni 3+ and Heresy have muting relays to avoid this sort of thing.