I'd compare the outcomes beyond accepted requests. Engaging first also selects people who post regularly, so an apparent improvement could partly come from comparing different kinds of prospects.
A useful test would be to take two small, similar groups in the same role and industry, use a clear professional reason for every invitation, and track actual conversations after acceptance. Count the time spent engaging as well. That would tell you whether the extra step helps your particular networking goal, without assuming a higher acceptance rate always means better connections.