If you're using it for clays and not for hunting, I'd give it a few runs and see what happens...you might not want the chokes installed.

Assuming the barrel is properly shortened, there isn't any problem shooting it, but it will be a pure cylinder bore shotgun.

Yes, it is possible to have new chokes installed, yes, it'll likely be about $100, but that includes the chokes he installs...I've had a few shotguns recut (or cut for the first time) for chokes, the most I've paid is $110, and I got an S, I, M, and F set of chokes to go with the job.