I'm not creating a community. I'm creating a new communication site for an existing offline community. 

The point is to make communication easier. Next is to make it secure. If it's not easier, they will continue to be frustrated that they can't just use email.

Is it possible to let us choose whether or not new conversations alert members?

At present, if I start a new conversation with a member, then I have to send a reply to that conversation to get them to log into the site to see the conversation.

We will end up abandoning that module if it cannot be changed.