Does any forum script provider also provides ready made auto responder with them?
Paid ones do. Such as Xenforo or vBulletin. But I will recommend that you use any third party service for this. In this way you will be independent about mailing.
Even though many forum script providers will do provide the service. But you should definitely consider getting a separate ESP. That's the wise choice to make.
I would like to ask OP why would you want it anyway? Is there any point or objective to it?
I just asked because if they are from one platform then wouldn't that be easier to mass email the members?