yes

What do you want to be the focus here; the shelves/contents or the beam/bulkhead? I would want all the shelves to match and that would put the focus on the decor rather than the big architectural imposition of the beam. Find skinny lights that can be mounted on the actual shelves rather than on the crown above. How wide are the shelf openings? Maybe we can help you locate something suitable.

We used phantom lighting on our shelving units, they allow the shelves to be adjusted yet still have lights on each shelf. The lights are led strips that are mounted behind the lip of the shelf, you can't see them. Love them. https://www.phantomlighting.com/products/cabinet-lighting/

Thanks for the input... for those saying yes... do you mean "yes it will be unbalanced, do it anyway" or "yes it will be unbalanced, don't do it."

The focus of the lighting is just for a little ambient lighting, and to feature what is on the shelving.

If you skip putting a light on the shelf with the bulkhead, people will tend to look at that because it is not like the other shelves. Draw their eyes to the decor and shelf, not the bulkhead. Without lighting like the other shelves, that one will be a black hole and make the whole area look wonky.

Picture lights always look effective. I like those provided by https://perfectpicturelights.com/ . Nice design and perfect quality