According to the databook, Unohana is one of the strongest captains in the Gotei 13; the only captains with higher stats than her are Yamamoto and Aizen. The book also states that she is a highly proficient swordsman, I think it might have even specified that she uses Kendo, but I'm not sure. So yes, I am sure that Unohana is quite capable of fighting - she would not have been made a captain if she weren't capable. However, she tries to avoid violence because of her philosophy as a healer, such as when she encountered Rudobon in Hueco Mundo.Yes Unohana can fight.