It depends somewhat on circumstances and age, but I think falling asleep while socializing is typically rude. At a large family gathering, it is, to me, less rude than at a dinner party.
In general, if she was invited over to socialize and he is that tired, he should probably go to bed, rather than sleep in front of her. It also suggests that she has overstayed her welcome if the host is falling asleep in front of her.
If he is visiting her, then he needs to excuse himself when he is getting that tired and say it's time to go home.