Can MC cable be ran in a finish brick wall to a light fixture with no box or shorting bushing, just cut off flush with the brick and light fixture used for the box?

I see installations like that terminating in a pancake box.

A rotozip with a tile bit is needed for this job. Trace the outline of the box onto the brick, and cut the box into the brick flush, which will result in a better fit against the surface for most fixtures. Some fast hardening hydrallic cement to affix the box. Lawyers will not always be necessarily nice to you in a court room if you skip on the box.

A tile bit will cut the brick? If that's the case, I'll have to remember that for next time. Those rotozips are a great tool to have.

Rut,
300.15 requires you to install a box at your fixtur splice point.

Short answer to question. No.