NO, Droppers are not allowed for KVPY.Only currently enrolled students are allowed to appear for KVPY.
If a student want to appear for KVPY now then they can appear for Stream SB: Students enrolled in the 1st year of undergraduate program in Basic Sciences namely Physics/Chemistry/Mathematics & Biology leading to B.Sc./B.S./B.Stat./B.Math./Int. M.Sc./M.S.