If your table has a PK field set to not allow dupes, then what about suppressing the error message you'd get when you try to append duplicates in the field? I don't usually advocate turning off warnings, but have done so for cases like this. The allowable data was always appended and the duplicates were not. Just don't try to use an append sql as a row source and make sure your code turns the warnings back on in the same procedure. An error handler is advised to facilitate this should an unexpected error arise. I can't recall if I ever tried this with the Execute method, but I think not. IIRC, that method stops if an unhandled error is raised, so only part of the data would get processed.
The more we hear silence, the more we begin to think about our value in this universe.
Paraphrase of Professor Brian Cox.