I can give you my experience: I left BCG in 2013 to join McKinsey. As a consequence, I was still listed in he BCG alumni directory, but I could not use the full functionality of the alumni website/platform (e.g., I could not search for alumni, I could not see job postings etc. I would also not get invitations for BCG Alumni events; however, other BCG alumni could see my profile and some reached out with specific questions over the years). BCG explained to me that this is their policy for all alumni who work for direct competitors.
I left McKinsey a couple of months ago, and as a consequence I was "upgraded" to a full member of the BCG alumni community.
Hope this helps! Sidi