No. Archive mode concerns redo logs, flashback doesn't operate over redo logs.
There can be a flashback data archive (sometimes called Total Recall), but even if there isn't, flashback can always use undo. Besides, when the data needed for the flashback is no longer in the undo, an error occurs. Otherwise you couldn't distinguish a table that was empty two minutes ago from situation where there are no data for the table at two minutes ago.
I just did a quick
test that shows that a missing commit is a problem: