Even though weed calms the stomach, I think it has more to do with the overwhelming (and this may be an understatement) spinning feeling. I think that when you feel this feeling of too much weed and alcohol, any stomach calming effects of weed are lost to the overwhelming sensation...
If I am really stoned, and I drink, I will probbaly only have a few drinks for a nice potentiation of the buzz. But if I am already heavily buzzed or drunk, and start smoking there is no way I can keep from getting sick.
To answer the poster's question, I think that beer before weed is more likely to make you sick because what seems like a mild alcohol buzz alone oculd be disasterous when mixed with weed. So if oyu are drinking first, you will probably not stop until the effects of alcohol are too strong for the mix. Then of course, being drunk or buzzed, you will feel in a party mood and smoke up, then get sick....
If you get stoned first, as the primary weed effects start to decrease and you start drinking you would be more likely to feel if it is coming on too strong and stop.
But I would say this is by no means fail safe. If you get extremely stoned (especially with a low tolerance or little experience), then proceed to hammer down shots or chug a ton of beer, I would assume you woudl be quite likely to get just as sick as the other way around.