Yep, probably. They get the weapon their Susanoo have. The Susanoo user can switch weapons it want to use. Also, for using weapons, it must be a V3 Susanoo.
Also, About Itachi's Susanoo weapons, they are legendary weapons, Totsuka Sword, which seals everything it pierces in a drunken dream world, and Yata Mirror, which deflects all attacks.
Since they are legendary weapons, there is a possibility that they can also we wielded be bare hands. As Orochimaru's Sword of Kusanagi.
Other susanoo that have shown weapons:-
-Sasuke's -
1. MS Version- at his MS susanoo, it had a bow and a arrow, however, it can also use sword.
2. EMS version - His EMS version susanoo has a black orb of amaterasu at one hand of susanoo, whereas bow and arrow coated with amaterasu flames in other.
Madara-
1. EMS susanoo- His MS susanoo have 4 hands, having normal curved swords.
2. EMS susanoo(ultimate version)- It has 4 big katanas on two sides of it.