Would taking AP stats along with precalculus be difficult? Moreover, would doubling up be worth it?
Difficult? It depends on how well you do in math. Worth it? It depends on the context of the overall schedule and what you want to do in life.
Most people at my school take them concurrently.
I’m taking AP Calculus and AP Stats in the same year. It is challenging but defiantly worth it. Colleges will see that you have good initiative and that you strive to challenge yourself. Work hard, and it will defiantly pay off 
Im currently taking precalc honors and AP stats. i wouldnt say its overwhelmingly difficult, but it is challenging. it really depends on the person though. i find precalc a lot better and easier than ap stats but i know some people who disagree with me. just dont expect to go into ap stats and do a lot of math like precalc math, because sime chapters of ap stats have no math at all and just analysis. def worth it though. PM me if you have further questions!
AP Stats doesn’t get very advanced in terms of math background required (you only need understanding of basic algebra), so taking AP Stats with pre-calculus is doable.
However, if you want to actually understand some of the topics (e.g. the normal distribution, or the central limit thm.), knowledge of calculus and more advanced topics is recommended.