Yes, of course ! . In my opinion, it is best to drill first, then cut into the lengths that you want, then assemble onto the brass tube, gluing each newly added piece to the previous assembly. . This will give you the horizontal stripe effect that you want. . You can make all of the pieces the same length so that the stripe widths are all equal, or you can vary the lengths to achieve variety or whatever effect you want.
Of course, you should calculate ahead of time what widths you want. . Also, you have to allow for the kerf width of your saw blade in order to get all pieces to the length you want. . You can, of course, choose to randomize the lengths and/or just slap things together and take what you get.
Be aware, also, that gluing end grain to end grain can form a fairly weak joint. . So do a bit of planning and use the brass tube to strengthen and keep the assembly together during the assembly/gluing process. , You don't have to glue end grain to end grain ... you can do anything you like and get a rather creative effect. . There are no set rules.