I have done graduate admissions for my math department. I am a "pure mathematician" but my department is just the math department: there is no formal separation between pure and applied.
Others can speak for themselves, but I always find honesty refreshing, and the idea that a prospective PhD student does not want to pursue an academic career does not horrify me: rather, in some ways it relieves me. Moreover, if you know this "all along" and don't disclose it right at the outset, when will you disclose it? There is no natural time until you are graduating / going on the job market, and then it will be way too late for your programmatic experiences to be tailored to your true goals.
The worry here, I suppose, is that you risk looking "less serious" than other applicants. In my opinion you can completely counteract this by including, a plausible, specific post-PhD career plan in which having a PhD plays a natural role. That is, don't say "I don't plan on pursuing an academic career" or even "I plan on pursuing an industrial career", say which industrial career you are aiming for and why the PhD will be helpful and/or necessary. Math PhD programs would like to have students with specific, realistic future plans that they can work towards steadily during their time in the program. We don't see many such students, but we would like to have them anyway.