I mean, it took Admiral Jellico and a direct order to keep her from violating the Romulan Neural Zone. My initial response to this is that she will go to quite extensive lengths.
Actually, it took her first officer to stop her from following the ship into the N.Z. initially. She consuled with Jellico afterwards.
Also, she was working under less than accurate info at the time and I think she kept a rather objective head in the matter, considering that she was more concerned about KIDS being in control of the Protostar and this unknown weapon onboard (which she voiced to Jellico - and the matter was indeed quite serious).
It was Jellico who inferred her judgment is clouded due to Chakotay... which I also think is accurate to a degree.
There's no doubt in my mind Janeway will go to significant measures to rescue Chakotay, however, she also lives in the moment and focuses on that moment quite well... and she's not in the DQ anymore... so she will have to consider all the options.
But I think even Jellico might approve of her rescue mission for Chakotay and his crew... or she might go directly against him and risk demotion on that matter.