Are women to wash with a blessing even if they will not be Davening Shacharis?[1]
Yes.[2]
[1] Bach 4; and so is implicit from all Poskim that did not differentiate in this regard. See Ishei Yisrael 2 footnote 93; However see Michzei Eliyahu 1:11; Birur Halacha 4; Meorer Yisheinim 23; Piskeiy Teshuvos 4 footnote 7 that rule a blessing is not to be said if one will not Daven.
[2] As they too will at least recite some prayer throughout the day, such as Birchas Hashachar and the like and hence fulfill the Biblical command of prayer. Furthermore, as rules the Bach, the Sages did not differentiate and state that one who will not be Davening [such as women, children and the ill] do not have to say the blessing, as they made a Lo Plug. This especially applies according to our custom to always recite the blessing of Al Netilas Yadayim even if one did not sleep at night and there is no evil spirit, as will be explained in Halacha 16. Those Poskim of today that rule a blessing is not to be said is because they hold Safek Brachos Lihakel as perhaps the main reason for the blessing is as rules the Rosh. However according to Admur which rules like the Rashba there is obviously no room to say that women do not have to say a blessing.