Will afterburner work at settings less than full dry thrust?
Afterbuner simply injects fuel directly into the jet pipe (i.e. beyond the turbine) in order to greatly increase thrust. The way throttle levers are normally set up, afterburner is engaged once the lever is advanced past maximum dry thrust, but I can't imagine why, theoretically, you couldn't set one up to be engaged at less than maximum dry thrust.

Mind you, it would be awfully inefficient to do so, as thrust output is exponential, with most of it being delivered in the top 5% of the RPM band; engaging afterburner while you still have a lot of dry thrust available would just be a massive waste.

What's more, jet engines are much quicker to respond today, and, in addition, landing approaches are not performed at idle thrust; the main benefit of flap settings greater than 20 degrees is that they slow the aircraft down, allowing for steeper approaches. In jet aircraft, this also allows the engines to be kept spooled up above flight idle, specifically in order to reduce response times in the event of a go around. 
In other words, throttle might be reduced to flight idle for the initial descent, but the final approach will use a higher thrust setting. 

The benefits of adding afterburner to civilian transport aircraft are usually massively outweighed by their costs (see the Concorde and Tu-144).