Most doubles can be fitted with a scope. If the dovetails aren't already there, they can usually be cut. The best way, by far, to mount a scope on a double is the claw mount, but many recoil at the cost. Given what a nice double costs to begin with, I can't say that I've ever understood that.

I've handled DRs with scopes mounted by NECG, and would not choose that shop for the job. My choice would be J. J. Perodeau at Champlin.

Yes, the weight of the scope can change regulation, sometimes a lot, and don't let anyone tell you otherwise. This varies from rifle to rifle. For some reason, it doesn't affect the regulation of some at all, but others it certainly does. I probably wouldn't scope a double that I didn't intend to use primarily with the scope, so, if I scoped one, I'd have it regulated with the scope. Chances actually aren't that bad that you won't have to re-regulate, but don't count on it.