The chemistry of ascorbic acid in preventing oxidation in white juices and wines is complex and this has led to confusion about its effectiveness. When used alone as an antioxidant, ascorbic acid reacts very rapidly with oxygen and thus retards oxidation. However, the reaction of ascorbic acid with oxygen produces oxidative products that, in the absence of free sulphur dioxide, will in turn oxidize wine components. Thus ascorbic acid alone is not a suitable antioxidant in winemaking.https://books.google.com/books?id=0PHcCQAAQBAJ&pg=PA41&lpg=PA41&dq=ascorbic+acid+long+term+effects+on+wine&source=bl&ots=M29GY05dEh&sig=OuLphI9YzY6iO5_7-7w7K0SYMKU&hl=en&sa=X&ved=0ahUKEwjTkuPQ8azTAhUL94MKHdzBC9sQ6AEIKjAB#v=onepage&q=ascorbic%20acid%20long%20term%20effects%20on%20wine&f=false
Free sulphur dioxide does not react rapidly with oxygen, thus it is not a good oxygen scavenger and does not fully control wine oxidation. However, the combination of ascorbic acid with free sulfur dioxide is a very effective antioxidant, even in the long term, provided that a level of free sulphur dioxide is maintained in the wine. The ascorbic acid reacts rapidly with any oxygen present and the oxidative products in turn react with the sulphur dioxide and are eliminated.
This has probably been discussed before...
Though this refers to wine, it's within the realm of possibility to think that some of the same applies to beer. If the SMB reaction produces Sulphur Dioxide and Ascorbic Acid (AA) is used then there should be no negative effects, however if the SMB does not produce Sulphur Dioxide and Ascorbic Acid (AA) is used then there would additional oxidative products from the AA. Using AA alone would certainly leave oxidative products and not be appropriate for long term storage.