Depends - as I learned when I moved to the US at least some of my mental maps are based on where the sun is in the sky (and the sun and moon are upside down there) took me a few months for it to all turn around in my head, there are still parts of the first places I visited which are backwards in my mental maps 40 years later
In the sense of not knowing where they are in (say) germany, a country they've never visited, then "yes" they'd "fail".
They might even have to resort to pulling out their iPhone and ringing a relative who's living in Germany.
In the sense of not being able to survive in a Mexican desert if they were originally a desert dweller .. then I suspect they'd get by - ditto coastal, river, forrest, dwellers.
Survival skils transfer well enough across known similar habitats, a western desert nomad would be on the tough end of a learning curve in Alaska.
I mean that they would lose ability to tell where is north. Because theoretically, but probably not in practice they could have some sort of magnetic sense like birds are thought to have so it would translate beyond hemispheres. But unlikely since they never needed cross hemisphere ability. Also haven't heard of people developing a magnetic sense so far.
But I do think some mammals may have magnetic sense so maybe...
I specifically meant fail as in ability to determine north, not survival, put down or any sort of other negative reason to be clear.
> I mean that they would lose ability to tell where is north.
You're aware, I trust, that the sun rises in the east and sets in the west, regardless of hemisphere?
FWiW this isn't a theorectical "what if" .. right from the get go Europeans were taking southern hemisphere indigenous people to the northern hemisphere: