Q. Someone who is preparing himself to become a Ger and is already enrolled in a learning program, is in contact with the Beis Din and attends regularly a Shul, ….If he owns a lulav and esrog can he do hakafos around the bima or the mitzvah of Hoshanos?

A. Poskim disagree as to the value and worth of a voluntary mitzvah performed by a Ben Noach or Gentile. Rambam (Melochim 10: 10) rules that it is considered a mitzva and is accepted as would be his korban and his tzedaka and help to the poor.

Responsa Maharam Alshich (110) rules that while women according to Rabbenu Tam and others can perform and recite a brocho on mitzvos that have time restrictions making them exempt, a servant (eved k’naani) should not. The reason, he explains is that women have kedushas Yisroel and although they are exempt from the obligation of performing those mitzvos, if they observe them they comply and the mitzvah will be rewarded. The same does not apply to an eved k’naani and certainly not to someone who is still a Gentile. (See also Kovetz Shiurim, Kidushin 142- 144, Mishpetey Uziel 3: C.M. 3, and others)

Similarly Igros Moshe (Y.D. 2: 7) maintains that donning Tefilin, wearing a Talis, sitting in a Suka, holding a Lulav, listening to the Shofar, eating Kosher or avoiding Shaatnez has no meaning and therefore no reward for a Gentile, since they were not instructed to follow those commandments. He differentiates between other mitzvos such as helping others or honoring Hashem or parents, where they have a share and are rewarded.
Teshuvos Vehanhogos (1: 614) distinguishes between the intentions of the performer. If he observes the mitzvos thinking that other nations also has been ordained and obliged to do the mitzvos given in reality only to the Jewish people, then they carry no value. However, if he understands that his compliance is only voluntary he will be rewarded.

Sefer Chasidim (690) maintains that from the time a Gentile has determined in front of a Beis Din that he will convert to Judaism, he should refrain from eating non-kosher foods. It is usual today for a prospective ger to comply with most mitzvos in order to become familiar with them.

Horav Shlomo Miller’s Shlit’a opinion is that he should avoid the hakofos with the Lulav or the Hoshanos, which are done publicly (see prior question as to the pertinent issues involved)

Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit”a