Thanks for asking this question.

Sen's central result is that his approach to formulating the action in the Ramond sector is consistent. That is, the spurious degrees of freedom he needs for the Ramond action decouple at the loop level. For Type II superstrings, we probably can't do much better than this because the self-dual five form resists a Lagrangian description. For heterotic strings and open strings, there may be better options. See the recent paper by Okawa and Kunitomo.

Sen does not actually go very far towards constructing the Lagrangian. But he has an argument that in principle one can find a set of closed string vertices which satisfy a set of algebraic relations which imply gauge invariance. This is an argument he has been developing, at some points in collaboration with E. Witten, over the past 2 years or so.

I do not know how much one can learn about nonperturbative string theory knowing the existence of such a Lagrangian. To me, it seems we do not know much more about the Lagrangian than a set of algebraic relations which have been known since the 90's, and in any case were generally expected to apply to superstrings. But I wouldn't underestimate A. Sen. I am most excited to see where he goes with this.