Will afterburner work at settings less than full dry thrust? Dry thrust is normal jet engine power without using an afterburner. Max dry thrust is the engine's most powerful thrust level without afterburner.

But what if the engine is at half power, or even idle power? Can you safely engage afterburner at that point?

I'm interested in turbojets and turbofans. Both can have an afterburner. I'm wondering if it's possible to engage afterburner on both of them at a time when the engine is not already at full dry thrust.

Edit: one reason it might not work is that idle thrust might not be powerful enough to ignite the fuel in the afterburner.

The reason I ask is for emergencies. Jet engines need several seconds to spool up from idle to full thrust. If you could engage afterburner from the get-go, you could be up to max speed much quicker.
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).