I can confirm.
dhcp supplies search domain as follows: private blah.private blah.com (Verified with packet capture) resolv.conf is set to: search private blahprivate blahcom .4478] device (wlan0): Activation: starting connection REMOVED .4479] audit: op="connection-activate" uuid="2ff27172-df96-481f-be46- 3ea63171ca90" name="Z415402306130" pid=2694 uid=1000 result="success" .4481] device (wlan0): state change: disconnected -> prepare (reason 'none', sys-iface-state: 'managed') .4489] manager: NetworkManager state is now CONNECTING .4494] device (wlan0): state change: prepare -> config (reason 'none', sys-iface-state: 'managed') .4539] device (wlan0): new IWD device state is connecting .4822] device (wlan0): Activation: (wifi) Stage 2 of 5 (Device Configure) successful. Connected to 'Z415402306130'. .4831] device (wlan0): new IWD device state is connected .4838] device (wlan0): state change: config -> ip-config (reason 'none', sys-iface-state: 'managed') .4850] dhcp4 (wlan0): activation: beginning transaction (timeout in 45 seconds) .5240] dhcp4 (wlan0): option dhcp_lease_time => '259200' .5240] dhcp4 (wlan0): option domain_name => 'private' .5241] dhcp4 (wlan0): option domain_name_servers => '192.168.12.1' .5241] dhcp4 (wlan0): option domain_search => 'private blahprivate blahcom' .5241] dhcp4 (wlan0): option expiry => '1577091203' .5241] dhcp4 (wlan0): option host_name => 'w106' .5241] dhcp4 (wlan0): option ip_address => '192.168.12.106' .5241] dhcp4 (wlan0): option next_server => '192.168.12.1' .5242] dhcp4 (wlan0): option requested_broadcast_address => '1' .5242] dhcp4 (wlan0): option requested_dhcp_server_identifier => '1' .5242] dhcp4 (wlan0): option requested_domain_name => '1' .5242] dhcp4 (wlan0): option requested_domain_name_servers => '1' .5242] dhcp4 (wlan0): option requested_domain_search => '1' .5242] dhcp4 (wlan0): option requested_host_name => '1' .5242] dhcp4 (wlan0): option requested_interface_mtu => '1' .5243] dhcp4 (wlan0): option requested_ms_classless_static_routes => '1' .5243] dhcp4 (wlan0): option requested_nis_domain => '1' .5243] dhcp4 (wlan0): option requested_nis_servers => '1' .5243] dhcp4 (wlan0): option requested_ntp_servers => '1' .5243] dhcp4 (wlan0): option requested_rfc3442_classless_static_routes => '1' .5244] dhcp4 (wlan0): option requested_root_path => '1' .5244] dhcp4 (wlan0): option requested_routers => '1' .5244] dhcp4 (wlan0): option requested_static_routes => '1' .5244] dhcp4 (wlan0): option requested_subnet_mask => '1' .5245] dhcp4 (wlan0): option requested_time_offset => '1' .5245] dhcp4 (wlan0): option requested_wpad => '1' .5245] dhcp4 (wlan0): option routers => '192.168.12.1' .5245] dhcp4 (wlan0): option subnet_mask => '255.255.255.0' .5245] dhcp4 (wlan0): state changed unknown -> bound