If the long 'nose' of the coil becomes contaminated, this can lead to ignition current flashover external to the spark plug gap which results in a misfire. The ignition misfire occurs when the break-down voltage of this external path becomes less than the break-down voltage across the sparkplug gap. There will typically be evidence of these external flashovers such as carbon tracking on the internal nose and rubber boot of the coil.
However, I doubt that ignition misfires are the cause of your idle problem. The voltage required to fire a sparkplug gap increases as the density of the mix of gasses increases in the sparkplug gap. Gas density in the cylinder increases as engine output increases (larger throttle opening). If you are going to get ignition misfire because of an external flashover it will occur first at high engine loads. Problems at idle; but, fine at high engine load does not really equate to external coil flashover.
The only time it may be idle only is on a cold engine when you have accumulated condensation on the coil nose which causes flashovers which subsequently disappears as the engine heats up and the coil dries out. However, once hot the idle will be fine unless the coil has been damaged by the flashover in which case you should have a problem all the time.
You mentioned the sparkplugs being covered in corrosive dust. Is that dust just on the metal part of the plug or was it up the insulator? Crap on the metal part of the plug won't affect spark plug operation; but, is probably an indicator that you have a problem with the sealing gaskets on the coil covers which can lead to longer term problems if you are a keener that washes their engine regularly. Anything that appears on the porcelain of the sparkplug above the point where the rubber boot on the coil should seal against the plug is a problem and is likely an indication that the boot on the coil has failed. Since the boot is not separately available a new boot requires a new coil. When I install my plugs I lather the boot on the inside liberally with silicon dielectric grease to help seal the boot on the plug. It also helps to ease removal of the coil in 7 years because it reduces the tendancy of the boot to stick to the sparkplug.
Where the coil body rests against the head (around the mounting bolts) there are exposed coil laminations. If you have a moisture problem, I have seem surface corrosion on the laminations. Mild corrosion on the exposed lamination that can be removed with a scotch pad is likely a non issue (other than you probably have a coil cover gasket issue). If the corrosion is significant with evidence of migration to the laminations below and physical separation of the laminations, that can be a problem. It may not result in out right failure of the coil; but, may result in lower peak voltage capability. Again, this kind of problem would show up first at high engine loads, not at idle.