No. Joins in Rhino need to be “manifold”, that means that curves can be joined only by their endpoints and no more than two curves can share a common endpoint; surfaces must be joined by open edges and no more than two surfaces can share a common edge.
There are actually a couple of exceptions in the case of surfaces that allow you to have “non-manifold” structures (not recommended), but that’s not the case with curves.
–Mitch