I think the first four could be either a call that has not yet taken place or one that has already begun, while the second group of four suggest the call already is in progress.
in all cases, you could substitute him or her for you.
We're going to have you participate in a conference call
We're going to have you take part in a conference call
We're going to have you be part of a conference call
We're going to include you in a conference call
We're going to connect you to a conference call
We're going to hook you up to a conference call
We're going to link you to a conference call
We're going to tie you into a conference call