To the OP - heavy corrsion that weakens the case head would be an issue. What you show is cosmetic. Shoot it.
However, if a rifle has a tight chamber, light corrosion can cause chambering problems. Tumbling for a few hours might improve it.
As for tumbling loaded ammo: Powder will not break down. Fresh powder is tumbled for several hours as part of the manufacturing process to dust with graphite and in the hopes of rounding off some of the sharp edges on the kernels, so the powder will meter better. I am hard pressed to see much change. I have yet to see a kernel break in half from tumbling.