Cycling is an activated ability. Effects that interact with activated abilities (such as Stifle or Rings of Brighthearth) will interact with cycling. Effects that interact with spells (such as Remove Soul or Faerie Tauntings) will not.
If you cycle Ichor Slick, you may cast it for its madness cost. You choose whether or not to cast it with madness before you draw a card from the cycling ability.