RE: Is it possible to construct a meta_query with the condition
Yes, it should be. Change
"compare":"!=" in the same I gave.
RE: is it possible to update database table directly to update “Membership Type” = ‘Bronze’ if “Membership Type” is not specified (is null)?
Yes, but not a within Connections. You could use a DB tool such as phpMyAdmin, usually available in your web host control panel. You would have to custom craft a query to update the table and its value.
Hope this helps!