Can you lay bricks up right
In general, no. The reason is that you have quite small contact surface of each brick with the brick above or below, and also the vertical shape makes the wall less robust against shear stress (roughly speaking: force applied horizontally is multiplied by the height of the brick to compute the momentum, and the momentum is divided by the length of the brick to compute resulting forces in critical points).
However, for a small patch of bricks like you plan to do, this might be less of an issue. Still, you should interleave them, which means cutting them in halves for one of the two layers, that's not gonna be fun to do precisely.
I would personally still go for standard laying and make 4 layers by 215mm. Note that including the masonry mortar (I hope that's the right word for the glue you put between the bricks), that's basically the same size as stacking them vertically, and the wall will be stronger.