I would.
A SiL of mine broke a hip in France, where they have a 2nd home. Their own insurance covered everything after she finally left hospital, including IIRC an escorted return to the U.K. (Dbro had already returned) and an ambulance all the way back to their house.
Also, while we were staying at a BiL’s place in France a few years ago, a fellow guest was taken ill in the night. We visited him the next day in Dijon hospital (he wasn’t conscious) and the first thing I was asked was whether he had his own insurance.
Luckily he did - I had sat with him until the emergency services arrived, and he had told me where to find all his documentation.
Sadly, after a 2nd heart attack his life support eventually had to be switched off, but his insurance covered the return of his body to Scotland.