Would never work, EVER! Many of the teams in the AHL are in extremely small markets, that both can't sustain an NHL team, and don't even have NHL size arenas. Also, how on earth would the salary structure work, when you are paying millions of dollars in the NHL and much much less in the AHL. relegation works in Europe but most of those leagues, the salaries don't go as high as the NHL.
Also, free agents would never sign in the small market cities that comprise the AHL. Small market NHL teams, have a hard enough time attracting the top free agents as is. All this would ensure is that anytime the AHL team(s) came up to the NHL, they would get completely and utterly demolished and demoted the following year, and the NHL team that got demoted the year before, would tear apart the AHL and come back up the very next year. The talent level between the two leagues is immense!