No fast track.
If you are a couple, I suggest that one of you line up at immigration while the other go to buy the visa and joins you in the immigraiton lane with the visa.
The escort guys usually take you to the immigration booths on the right of the usual booths. They are designated for other visas and crew (or something like that) and tend to have shorter lines. But the escort poeple have no priority, so it is rather useless to hire them. Baggage for J pax is usually arriving very quickly and are collected by staff near a post designated CX Business class.
if you are in biz and among the first to get off the plane, the process can be fast. But if another big plane has just landed, then can be a long wait.