Closing your community down at the exact moment when people are most likely to begin using your products is nuts.
Closing your customer support line at the same time is even worse.
Ultimately, what is a customer support community for?
Is it for handling customer queries that slip through the usual customer service net? (perhaps non-standard problems, problems in different languages/cultures, support during out-of-hours moments?)
Or is it to handle the bulk of customer queries and leave the difficult personalized stuff to customer support? This means being as fast as direct support, ranking highly for relevant search terms, directing most people to the platform, being more accurate and communicating with greater empathy.