As long as it's showing the correct version (the update version), then yes.
Just an example to be sure I'm clear:
Timothy downloaded monkey ball a few months ago. His friends told him tonight that an update is out but can't see it and it's not asking him to update! On the monkey ball page however, it shows that the new version is available (1.1 - old version being 1.0). Timothy can click 'buy now', and it will re-download monkey ball and delete the old copy, thus leaving him with the updated version.