Nope.

Perhaps I should elaborate or this will be a very short article. Researchers at the Griffith University in Queensland, Australia (where else), set out to answer this very question. Beer is apparently a very popular post exercise beverage, just as Olympic Gold Medalist Jon Montgomery. Could low alcohol beer with added sodium be an effective rehydration beverage? Actually, this is the second time these same researchers tried this stunt. Again, their old friend XXXX light (2.3%ABV) and XXXX Gold (3.5%ABV) got a dose of sodium and was served to some lucky, dehydrated university students. These poor students were stuck in heavy tract suits until they lost 2% of their body weight from sweating. Then they were given salty, low alcohol beer in approximate volumes to replace the fluid lost from exercise. Apparently the average fluid lost was about 2 litres, yuck.
After this torment, the researchers learned that beer was not an effective rehydration beverage. Even though the saltiest light beer (2.3%ABV with 50 mmol/L sodium) was the most effective, it was also the least palatable. By comparison Gatorade contains about 20 mmol/L of sodium, so this beer was quite salty. I shall continue to sit on my couch and rehydrate with a nice Gose.