In this work we study the phenomenological consequences of the dependence of mass varying neutrinos on the neutrino density in the Sun, which we precisely compute in each point along the neutrino trajectory. We find that a generic characteristic of these scenarios is that they establish a connection between the effective Delta m(2) in the Sun and the absolute neutrino mass scale. This does not lead to any new allowed region in the oscillation parameter space. On the contrary, due to this effect, the description of solar neutrino data worsens for large absolute mass. As a consequence a lower bound on the level of degeneracy can be derived from the combined analysis of the solar and KamLAND data. In particular this implies that the analysis favours normal over inverted mass orderings. These results, in combination with a positive independent determination of the absolute neutrino mass, can be used as a test of these scenarios together with a precise determination of the energy dependence of the survival probability of solar neutrinos, in particular for low energies.