In essence, they're trying to get "credit" for the paper that's currently in the pipeline, by essentially asserting that in between the time when you read the CV and take action on it (i.e. when they show up if hired, etc.) the paper will be in the published literature.
Especially for things like revise and resubmit, there's a pretty strong chance that that's true.
The pros...should be obvious given that reasoning. You're essentially giving a preview of your upcoming academic productivity, for work that's already been done, but hasn't yet hit the presses. Especially for junior people, this can be very influential - the number of papers and your publication record can change drastically depending on whether or not you include papers currently in the pipeline.
The cons...are primarily rooted in "I don't believe you." For an R&R at Journal Name there's a degree of credibility, but occasionally across people who give a journal name for papers that are in submission, and often they pick very fancy journals. The fact that you know how to work the submission system for Nature doesn't tell me anything, and can put off an aura of either trying to goose your stats in a way that rings false, or just that you're hopelessly naive about the quality of your work and where it belongs.