No, all the audio recording will be automatically moved earlier by input latency amount if the ‘Adjust’ option is enabled.
However that actually make an opposite reason why you need to move sometimes, if what you were hearing during the recording was perfect, then you don’t want to move it. But it moves earlier on playback by the option.
Good musicians subconsciously play/sing earlier when the monitoring is slow, in these case the position is already ‘delay compensated’ by human, cubase don’t need to shift that on playback. This is why you can disable the option.
Actually I run Plugin Alliances Gig Performer in parallel with Cubase from the desktop as a standalone, not as an insert . I have a couple of vocal presets with the plugins I would normally use on vocals. Gig performer shares the input from my vocal preamp I monitor Gig Performers output through my RME Total Mix together with the Cubase Stereo out. There is very little latency, it is hard to tell. My vocal is simultaneously recorded in Cubase with the track monitor switched off. I have the same plugins on this track. So when I have finished the vocal take I play it back and it should sound as I have monitored it.