That approach could work, but you have to do some calculations on how much to translate for each step. I'd recommend generating the extruded geometry in a smarter way, though.
For example, you shouldn't draw the box caps (floor and ceiling) for in-between boxes. You also have to make sure the sides touch perfectly or you will get artifacts.
I recommend using a path to determine the planes where each set of vertices goes. The path should consist of a series of points and an orientation vector for each point, that determines how much to rotate around the direction vector. With that, you can calculate the 4 ring vertices very easily, just using basic vector math.
So, for example, you start with the cap [(0.5,0.5,0),(-0.5,0.5,0),(-0.5,-0.5,0),(0.5,-0.5,0)] and move it along the path (first is center point, second is right vector) [(0,0,0),(1,0,0)],[(0,5,10),(1,1,0)],[(10,5,12),(0,1,0)]
Now, you first calculate all three orientation vectors. The normal is the difference between the current and next point, so (0,5,10) - (0,0,0) = (0,5,10). The right vector must be projected onto the plane defined by the normal, so we calculate the up vector first using the cross product: (0,5,10) x (1,0,0) = (0,10,-5). And as a last step, we calculate the projected right vector, which is the cross product between normal and up: (0,5,10) x (-2,4,-2) = (-125,0,0). All three vectors must be normalized then, and if you put them side by side, you will get a nice transformation matrix that you apply to the cap vectors, yielding the 4 vertices for the current step:
|-1 0 0 | |0.5| |-0.5 |
| 0 0.894427 0.447214| * |0.5| = | 0.447213| etc.
| 0 -0.447214 0.894427| |0 | | 0.223607|
(I've probably messed up with the signs a bit, you might have to swap the cross product factors to get the right results)
Then you repeat the same procedure for each step on the path and draw the 4 ring quads each time.
