Hi,
Translations may still be broken for a specific language because it has not been fully translated yet. We are approving translation submissions as fast as possible.
In general, however, yes you can just export .mo and .po files directly from http://translations.theeventscalendar.com and replace the pre-existing files for that language in your plugins /lang folder.
Thank you all for your patience while we receive translation submissions and work through the approval process for them one at a time. Thank you!