That would depend entirely upon the quality of the establishment. Should such a thing ever happen to me in my usual watering hole, I would be carried gently to the bathroom and bathed by willing manservants. In a Wetherspoons, I suspect I would be battered senseless by the shaven-headed yob next to me.
I'm not sure you're right. Short of declaring a major medical emergency and calling an ambulance, I don't think any effective social mechanisms exist to deal with the eventuality of a grown man simultaneously puking and sh1tting himself. There can only be the terrible moment when everyone realises what's happened followed by panic.
To be fair, if I was standing at a bar and lost control of my bodily functions so catastrophically that I simultaneously vomited and moved my bowels, I'd want someone to call a fúcking ambulance. I mean, those sort of symptoms warrant more than some Andrews liver salts and a lie down, down't they? This is a case of dysentery at best!