My registered users want their own forum. Can it be done?

[Rokkojones]

My PHP/mySQL Linux website has members who purchase the product and then get access via their username/password stored in our database.

Can I install this forum so that - when they purchase product - they automatically become members of the forum with the same username/password as found in our database? Also the registration function on the forum will need to be disabled so that this is the only way to become a member of the forum.

Can this be done? Relatively inexpensively? I'd like to be sure before I purchase the forum.

Thanks.