Theoretically yes. The table shows all possible triangle topologies. The Metaball algorithm in Grasshopper uses a similar approach, except it relies on squares rather than triangles. Triangles are more flexible and allow for local increased detail, but they have more complicated adjacencies.
Even given the above outline, you still have to decide whether you’re happy to evaluate all triangles and collate the results afterwards, or whether you specifically want to trace the region paths across the mesh. The latter is faster, but more difficult and risks missing certain loops.
Do note that in Rhino you already have access to a Mesh/Plane intersection algorithm, so you could simply elevate the points to the appropriate value and then slice the mesh.
Also what sort of output are you looking for? Just polylines? Individual line segments? Does it matter whether a boundary curve belongs to the below-within or the within-above transition?