There is a similar trail that I tried in the past to bypass Madison. I have done various permutations of Madison & Adams from Appalachia through the years, one of my favorite descent routes is the Howker Ridge Trail. From Madison hut, I once tried to take the trail that tries to keep a relatively even contour around the north side of Madison to avoid going up & over the summit, I recall that not saving much energy if not being harder than going over Madison's summit, as the summit trail has much better footing. I would not take that trail again.
Sounds like you're describing the Pine Link (north of Madison). The Parapet goes to the south of Madison (which as David pointed out is a rough trail). It doesn't seem like Adams has any generally loathed trails to avoid the summit. The upper portion of the Buttress is pretty rough, but if you're looping Adams and Jefferson from the Great Gulf, you should be expecting some roughness.