It depends on what type of non-linearity you are looking for. And, which program you are looking at.
If you are looking for pure tension only behavior (member inactive whenever it goes into compression), the the program (RISA-3D) should handle that just fine.
Based on your description, however, you are probably looking for geometric non-linearity associated with the cable curvature.... meaning that the deflection caused by an applied transverse load will end up being resisted more through cable tension than through flexure/ moment. RISA-3D cannot generally account for that for cables.
Folks do occasionaly use the program for these types of applications, but it is a tedious process involving manipulating the input geometry to approximate the anticipated deflected shape of the cable. This procedure works in theory, but it's not something you want to do for much beyond verifying a calculation from another source.
For applications like this, it is generally a good idea to use a program which has an iterative / incremental non-linear solver that accounts for cable geometry. Programs like Tower Numerics (formerly RISATower and ERI-Tower) do this sort of thing for guyed monopole towers. That may be similar enough to your application to work.