That probably wouldn't work, I get hit with Chrome's red screen of annoyance regularly with stuff only reachable on my LAN. I suspect the trigger is that the URLs are like [product name].home.[mydomain.com].
Thus if I started hosting my Immich instance, I would probably put it behind "pxl.domain.tld" or something like that.
Not a garantee to pass the Google purity test, but, according to some reports, it would avoid raising some redflags.