Network Member / Site Member

I am starting project and need to confirm whether or not a network member is automatically a member of every site on the network.

Here are two scenarios:

A. Member joins through WPMU’s Membership plugin.

B. Member joins through one of the sites in the network.

My question considering the above is would the member be considered a member for every site on the network. If so, then if the member visits a different site on the network and that site say offers free listings for members – would this member be able to post a free listing? Based on, that they are a member that joined though a different network site.