The Modules do sometime fail, as to repairing the module, it all depends on whats wrong with it. If it something like a bad connection , then maybe yes, if it is a faulty processor chip, then no.
Usually a replacement item is required from a wreckers, but like I said, it may simply be a duff connector.
The fact that the dealer has admitted that there is a problem and is attending to it is a promising sign. If you run into too many problems, give me a call.
Hope your back on the road soon and loving your little Alfa.
Baz