An account having a dedicated IP has no bearings on the IP that is used to send out mail or make external connections from the server regarding that account.
Your server will have a main IP. This IP is used for all external outgoing connections from the server, regardless of what account on the server is sending out those connections.
So in short, if your main server IP is blacklisted, then it will affect all of the account on that server, even those that have a dedicated IP.
The dedicated IP function is only for incoming traffic to that server.