Seems like it. I brought another profile's hero with me into the RtR, and it told me for every chest that the other had not opened it yet. Might play thru on another profile just far enough to get the co-op achievements/[Spoiler? Highlight:demon door.]
Also, not done with first play-thru yet. Just became Queen. Sucked $$ out of the treasury for myself, gonna try buying.... ah.... every damn thing and letting the interest build for a bit. If I just check on home repairs every so often, hopefully that will get the Treasury back to where it should be.
Or I'll wager it all on a chicken race.