As a general rule, one may not recite a Beracha over a food or drink for another person unless he is also eating or drinking. For example, if somebody does not know how to recite the Beracha of "She’hakol," and he wants to have a drink, he cannot have his friend recite the Beracha for him unless the friend is also going to drink. If the friend is planning to drink, then he may recite the Beracha on behalf of himself and the other fellow, and then the other person answers "Amen" and they both drink. But if the friend does not wish to drink, he may not recite the Beracha for somebody else. When it comes to Birkot Ha’nehenin – Berachot recited over food or drink – one cannot recite the Beracha unless he is personally eating or drinking.
The exception to this rule is when the Beracha is also a Misva. For example, a person who had already recited Habdala may recite it again for somebody else, including the Beracha over the wine, even though he will not be drinking any wine. Since the wine is required as part of the Misva of Habdala, one may recite the Beracha over wine in the context of Habdala for somebody else, and that other person can then drink the wine. The rule of "Kol Yisrael Arebin Zeh La’zeh" allows one to fulfill certain Misvot on behalf of others, such as reciting Habdala for another person, and thus one may recite the Beracha over wine in Habdala when he recites it for somebody else, even though he will not be drinking wine.
There is a debate among the Halachic authorities as to whether this applies to the Beracha over the cup of wine used for Birkat Ha’mazon. Many people have the custom when reciting Birkat Ha’mazon with a Zimun for the one leading the Zimun to hold a cup of wine during Birkat Ha’mazon, and then afterward recite the Beracha of "Boreh Peri Ha’gefen" and drink the wine. Rabbi Akiva Eger (1761-1837), in his comments to Shulhan Aruch (190), writes that although the cup of wine enhances Birkat Ha’mazon, it cannot be considered a Misva, as it is not obligatory. Hence, one may not recite the Beracha over the cup of wine after Birkat Ha’mazon and then have somebody else drink the wine. Since this Beracha is not recited in the context of a Misva, the person who recites it must drink the wine. This is also the position of Rav Yaakob Haim Sofer (Baghdad-Israel, 1870-1939), who writes that one leading Birkat Ha’mazon must at least taste a bit of the wine, after which he may allow somebody else to finish it. The Be’ur Halacha (Rav Yisrael Meir Kagan, 1839-1933), however, disagrees. In his view, the cup of wine used for Birkat Ha’mazon is indeed considered a Misva, and therefore the one who recites the Beracha does not have to drink any wine, and may instead give the entire cup to somebody else to drink.
In light of these differing views, Hacham David Yosef, in his Halacha Berura (Siman 190, p. 533), writes that the one who leads the Zimun should take at least a small sip of wine, and he may then give the cup to somebody else to drink.
Summary: When the leader of the Zimun recites Birkat Ha’mazon over a cup of wine, he should drink at least a small sip of the wine after reciting "Boreh Peri Ha’gefen," and may then have somebody else drink the rest of the wine.