Whether a clematis would work around the unit or not is really going to depend on how close the wrought iron fencing is to the unit and how much exposure the plants would have to the air put off by it. I have evergreens (hollies and a chindo viburnum) planted around my A/C unit and have extended the condensate line to the base of a clematis planted on the exterior of one of the hollies. Sort of like having a constant drip irrigation system for that one clematis. That seems to be working out for that one clematis.

The other concern is how high is the fencing going to be. Trying to get a clematis to grow horizontally is going to require much attention since the tendency for the plant is to go straight up and to grow towards the sun.

Restricting airflow around an A/C unit is never a good idea. It will decrease efficiency.
So putting any type of fence (even one that has holes in it) and a plant would not be the best idea.

Cherry

You won't restrict air flow around an A/C with either a wrought iron fence which has holes for air flow or with plants if they are planted away from the unit to allow sufficient air flow. Shading the unit however will improve efficiency since the A/C unit won't have to exhaust the heat around it before it starts cooling your house. Ever noticed how much cooler it is in the shade of a tree versus the full sun? Same principle applies to the A/C unit. A unit sitting in hot sun will require more energy to cool itself down before it can begin cooling your house.