No, I don't think Badspot cares if you share the key between your household, hence he allowed LAN play. You only need one working copy of Blockland to play LAN, you don't even need a key to play on someone's LAN server, as long as they have a registered copy.
You do not need to use the same clan tags, by the way. I use USSR Wedge, and my brother goes by SNCK Wedge BAR.