Of course its doable. I use to shoot a lot of skeet and trap, and I used a 870. I had a 4 gun set in 410, 28, 20 and 12 gage for skeet and had a FC Trap barrel and trap stock for my 12 gage. Also had a Mec 600 JR for each gage, but my nimble fingers weren't too good at loading 410s.
The only disadvantage is the 870 has a little slower lock time then most skeet and trap guns.
All that met was you took a 6' o'clock hold on the birds instead of blotting it out.
I've had a heck of a lot of 100 straights in both trap and skeet (although not many with the 410 and 28 gage).
I'm not into shotguns any more but I still have my 12 and 20 gage 870s.
CPT USAR Ret
USAMU Sniper School Oct '78
Distinguished Rifle Badge 1071