Do old time present day active JWs genuinely believe in overlapping generations?
No they do not because the WT does not teach overlapping “generations”. They still adhere to the doctrine of “ONE” generation, but now the actual meaning of Jesus words “this generation” is no longer, “beyond question, that which takes a ‘generation’ in the ordinary sense”, but has now been stretched to include ‘anointed Christians’ born anywhere from the 1880s to the 1960s, so long as the latter overlap with the former while they where anointed.
It’s not incomprehensible, it's really quite simple, just total nonsense.
Last year I had a conversation with an ‘anointed’ witness who I have known since the early 1970s, and he claims he can clearly see the logic of this new understanding. Whether he actually believed that deep down, or was just paying lip service for my benefit I cannot say, but he seemed to genuinely accept it.