As far as I know, it is gramatically correct, but it does not sound the same (unlike some sentences like ils parlent vs il parle) so it will not be accepted. I highly suggest double checking with the slow version before submitting. My listening skills are pretty good, but with the robot voice, I've found it necessary for some subtlety.
Yeah, that definitely sounded like a "J" sound when she said "du". Got head phones on too.
Elmobites is correct.
In English we can use the verb "to have" to mean eating and drinking. We are having dinner (we are eating dinner) - he is having some wine (he is drinking some wine).
However in French the verb "avoir" can not be used in that way. In French a similar construction to the one you suggest could be gained by using the verb "to take (prendre)" to give "we are taking some wine" which (depending on the context) we would probably translate as "we are having some wine".
It follows therefore that in the example given in this exercise "il a du vin" can only mean that he has some wine in the sense of having it in his possession. We can not tell from the sentence what he is doing with the wine.