Is it even possible to clear an aircraft that is number two or greater in line to the airport for a visual approach if they don't have traffic to follow in sight?
No, the controller cannot clear that plane for the approach until he reports the preceding a/c in sight (that aircraft MUST have already been cleared for the visual approach, and you can link more the 2 or 3 together.). If the pilot is having difficulty finding the a/c, then the controller can either clear the a/c for an ILS approach, or have the pilot report the airport in sight and then clear them for a visual approach. If the latter is the case, visual separation does not apply, and the controller needs to ensure separation.
This brings me to an interesting side story which was debated on this forum before, but I can't find the thread.
Once, while listening to Kennedy Final, I heard a controller issue traffic to an aircraft for the purpose of having the a/c follow the traffic to final, just as we discussed above.
It was night time, and the pilot was simply unable to locate the preceding traffic. At this point, the final controller handed off the a/c to Kennedy Tower (without an approach clearance).
I immediately switch the feed over to tower.
The a/c checks on, and tower immediately asks, "Do you have the field in sight?"
The pilot responds with a yes, and the tower controller issues a visual approach clearance. Everything from this point on was normal.
I just thought this was the weirdest thing ever. I had never heard it happen anywhere before. But if I remember correctly, someone in the previous thread had explained it. Just though I would share that story.