One may not appoint a shliach to perform an action that one is excluded by halacha from theoretically performing for oneself. Tosfos (Nazir 12) asks how is it that ‘ma’aseim b’chol yom’, it is common practice for a woman to ask her neighbor to be mafrish challah for her even though she has not yet started to bake – until flour is kneaded into dough there is no chiuyv of challah and hafrasha cannot be done, so how can a women appoint a shliach to do what she herself is halachically excluded from doing? Rabeinu Tam answered that since the woman appointing the shliach can obtain kneaded dough and be mafrish herself, it is ‘b’yada’ to perform the mitzvah and the shlichus is valid. R”T compares this case to being mafrish terumah from harvested grain that fulfills the chiyuv hafrasha on a section of the crop that has not yet been harvested (kiddushin 62) – since it is in the owner’s power (b’yado) to theoretically harvest all the grain immediately, the hafrasha is valid.
Does the proof parallel the case of challah? In the latter case, both the harvested and the unharvested wheat belong to the same owner – the sevara of b’yado simply removes the obstacle of the still growing wheat not yet being chayav yet in hafrasha. The shlichus case involves far more than that. It is not only that the hafrasha is being done for flour, which is not yet chayav, but there is an additional problem of the dough from which the hafrasha is done being owned by someone else. Since it is not b’yado of a person to take his/her neighbor’s dough to do their own hafrashas challah, how can the shliach’s hafrasha using her own dough help the meshaleiach? (Ch HaGRI”Z Nazir 12 leaves this with no answer).