Like the rest of the guys here, I dont see a problem with tumbling brass for a while, as long as you dont let them tumble for long periods of time. Long tumbling sessions (like starting the tumbler and leaving on vacation for 2 weeks and forgetting to turn it off before you leave) may thin the body/shoulder transition of some of your cases.
Im sure theyll be bright though.
I tumble all my brass but I dont worry about bright and shiny. I worry about clean. If I get shiny brass thats just a bonus.