Q. One who did not wash, may he say one of the sheva brachos (whether by the chasuna seuda or during the week of sheva brachos)?

A. Poskim disagree if one can recite sheva brochos without having eaten by the seuda. Yabia Omer (3: 11), Cheena Vechisda (Kesuvos 1: 112b), Beis Chassonim (12: 6) quoting Horav Eliashiv zt’l, Nitei Gavriel (Nissuin 2; p, 232) quoting Imrei Emes and others maintain that one who has not eaten bread at the seuda, should not recite the sheva brochos. Pnei Yitzchak (1: Brochos: 101) permits if there is no one else that knows how to recite.
However, Yaskil Avdi (O.H. 8: 20: 25), B’eir Moishe (2: 118), Mayeinei Ayeshua (42b), Rivavos Efraim 4: 227) and others assert that even if one did not partake at all from the seuda, he may recite the sheva brochos. Sovea Semochos (4: 73) affirm that this is the common accepted minhag, Nitei Gavriel (ibid.) mentions that this is also the Brisker minhag.
Oholei Yeshurun (Sheva Brochos5: 9) cites Igrois Moshe that if one just eats or drinks something, without consuming bread, he may lechatchila, recite sheva brochos. Beer Moshe (ibid.) relates that this was the minhag of the Satmer Rebbe zt”l and other Gedolim.
Horav Shlomo Miller’s Shlit’a opinion is that it is preferable for one to wash or at least to eat or drink something, in order to recite sheva brochos, however if he didn’t he can still recite them.

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