An edge from node A to node B is just a property of node A. So assuming you have the default settings for this edge predicate, it will just be like setting a value on a bunch of unrelated nodes. It also matters what your insert pattern is (upsert mutation, @upsert annotation on predicate, blind writes). If you read a unrelated field to make the connection (eg: xid) then that could cause an abort if it changes.
I also assume you mean from 19000 different connections concurrently, as opposed to one transaction which you could do all of these in and definitely avoid any transaction aborts.