CSQC lacks any and all .movetype support (including thinks supposedly, though DP violates this and gives inconsistant behaviour between csqc and ssqc as a result).
It looks like twig requires think function calls, but movetype support basically just involves MOVETYPE_PUSH hacks. This means that twig should work in csqc despite the lack of movetypes, but you will need to emulate think functions somehow (again, DP breaks the csqc spec by supporting thinks anyway, but this likely means that it will 'just work' in DP's csqc).
Of course, objects which are solid in csqc do not affect the position of objects whose position is controlled by ssqc, unless ssqc has a duplicate of the object which is equally solid - I don't know how good twig's error correction is.