Is it rude to fall asleep during a massage?

no.

in fact, it probably means you received a really good one...

On the other hand, if that happened in the hottest massage parlour in town ....

Wrong question. Should be Is it rude to farts during a massage?
These things happen given the human condition. Still would be mortally embarrassing I bet.

Depends on the farter. My youngest was having a meal with my oldest and a bunch of friends to celebrate a birthday. Afterwards they were outside talking when someone remarked on a foul smell, thinking the sewers had been taken up. Now the youngest had farted and when challenged he said he was proud. Needless to say the crowd quickly dispersed. Now, every time he meets someone from the restaurant party he reminds them of how his fart cleared the street.

That depends on whether you are giving, or receiving the massage.