On this daf, we find a discussion of precisely when one is considered a convert.
Nearly one hundred and fifty years ago, long before the contemporary teshuvah and giyur explosion, a very special soul lived. Born to non-Jewish parents, he felt very drawn to Jewish practice and decided to convert. He was told that the most prestigious bais din was in Yerushalayim, so he undertook many weeks of arduous and dangerous travel to pursue his geirus in the holy city. On Tuesday, the twenty-third of Adar Sheini in 5708, he underwent milah. The doctor forbade him from immersing before his wound healed completely. By Shabbos, it was still not fully healed and he had not yet immersed.
Nevertheless, the ger was thrilled to be able to keep his first Shabbos. He was so enthusiastic that he told everyone he ran into on the holy day. When the rov heard about this, it was already after Mincha. He sent a message to the ger explaining that since he had not yet done tevilah, it was still forbidden for him to observe Shabbos fully. The ger understood and immediately wrote a few words in order to violate Shabbos.
The next day, when the other rabbonim of the city heard this, they took this rov to task. “The custom has always been to allow such a ger to observe the Shabbos after he has done milah, even if it before tevilah.”
The rov protested: “But in Shulchan Aruch we find that one becomes a ger only after he did milah and immerses with the intention of accepting the mitzvos.”
The other chachomim of Yerushalayim rejected this out of hand: “But the man has done milah and accepted all mitzvos. He is only waiting to heal to complete his conversion. Since there is no source that such a person may not keep Shabbos and the custom was that he does, you are obviously mistaken.”
When their question was presented to the Binyan Tziyon, he agreed that the ger should have kept Shabbos: “Although on the surface it appears that even such a ger should be forbidden to keep Shabbos, the custom here as well is to allow him to keep Shabbos. Although you make a good point, I believe that Tosafos in Kerisos indicates that you are incorrect. There we find that from when our ancestors did milah, they were considered to have entered the bris. Clearly, one who has done milah in order to accept Torah and immerse is already separated from the non-Jews. It follows that he can keep Shabbos” (Shu”t Binyan Tziyon 91).