Does one have a chiyuv to say birchas hatorah if he isn't going to learn anyway that day?
There is a chiyuv (obligation) to learn Torah each day, so one already has a chiyuv to say birchas haTorah.
Regardless, I assume you'll be saying the bits of Bible and Talmud (Yevarech'cha Hashem ... Eilu devarim sh'ayn lahem shiur ... eilu devarim she'adam ochel) that come right after the blessings? That's Torah. The Shema? That's Torah. Without trying, you'll wind up reciting some Torah sooner or later!
But yes, it's part of the daily blessings no matter what you intend to do that day, so say birchas hatorah.
It's even suggested that our entire daily routine is considered one extended act of "involvement in Torah", as how you eat, work, talk -- are all governed by Torah. (Hence only one bracha needed per day.) Or as one yeshiva put it: "some yeshivas think Torah is everything. We think everything is Torah."
Shulhan Aruch Y"D 246 says one must learn Torah, no matter what their financial position. In some siddurim they bring some baraytot and pesukim to say to fulfill this obligation.