Does applying to one of the 4 joint programs in undergraduate Wharton at UPenn make it harder to get in than if you don’t apply to a joint program, but restrict yourself to Wharton?
Yes. But you have the second chance for a regular program when applying to a joint degree program.
I think I’m interpreting the question differently from @coolweather. The dual degree is harder to get into than regular Wharton, but it doesn’t hurt your odds of getting into regular Wharton (if you get rejected from the dual degree), so it should have a neutral impact on your odds of getting into regular Wharton. That said, I’d only advise you to apply to a dual degree if you are genuinely interested in the two fields of study.