I do believe the answer is no. There just isn’t enough alcohol to affect your system. I recently saw a video where Tim “Eater X” Janus was trying to drink enough beer in an hour to be legally drunk. He drank 28 beers and achieved a 0.02 BAC. It is difficult to predict exactly what your blood alcohol content will be after consuming alcohol because it depends upon what you ate prior to drinking. Greasy foods tend to slow down the absorption while an empty stomach would lead to quick absorption.
I’m not quite sure how he calculated the alcohol. I found an online calculator which puts it at 5 beers in an hour, but they do not list alcohol content. I found another which put the number at 5 beers in an hour to be 0.087 and at 4 beers to be 0.066. So if 60 ounces is 0.087 to have a BAC of 0.08 you would need about 55 ounces of beer or 4.6 beers. So let’s do the math on 4.5 beers and call them 5% ABV. The O’Douls in the video link is 0.4% ABV and he drank 28. So he had an equivalent number of 11.2 units. 4.5 beers equivalent units should be 22.5 (4.5 x 5). He only blew a 0.02 which brings into question the accuracy of the meter and the accuracy of the ABV representation in the NA beer. Also it takes some time for the alcohol to influence your system so it would have been interesting to see how his BAC increased in a half hour. Anyway, in order to be drunk on O’Douls it seems to me he would need to have over 56 of them in an hour and I don’t think it is possible for anyone to consume 672 ounces (5.25 gallons) safely.
Don’t try this at home, the bottom line is you cannot get drunk on NA beer. You may have water intoxication, but that has nothing to do with alcohol.