Sorry, just noticed this q hadn't had a response yet. I'll share some thoughts here...
Regarding your overarching question - there's not really one specific right answer. It depends on your ultimate goals. What's most important is to craft a business plan around your community, and within it to document your goals. If those goals lead to driving customer loyalty and are all about improving the customer experience post-sale, then it might make sense to keep it closed. However, ultimately it makes it more difficult not only from an SEO front but just in illustrating to prospective customers one way that you are helping them post-sale. You definitely will not see as many WOM, SEO, or other marketing benefits by keeping it closed.
As an aside, we're making some changes to Clearstep and one of those is making it more open. That is, we're considering to not require registration in order to participate. Sometimes it's just too high of a barrier. In this example, your question didn't get answered - however, possibly if we didn't require registration, and then post your q to the twitterverse after a given time with no answer, then it's likely your q could have already been answered. Anyway, just trying to use this thread as an actual example around driving further engagement by making the community more open.
Without full context private communities are the worst case scenario. We (Intel) have one only for legal reasons to share information that is "confidential".
If your topics are not "confidential" then I recommend keeping the community open. As Adam mentions, among other arguments, folks hate to register let alone login to get information. It is in a sense "anti internet" (cognitively speaking).
If you want more input feel free to call me. 503 724 2876.