I would recommend reading the ammunition guidelines in your users manual, as it should work, but it is always good to check with the manufacture.
The 17 HMR is a different cartridge than the 17 Win supermag.
As illustrated in the linked picture.
https://www.huntinggearguy.com/wp-content/uploads/2014/08/17-WSM-vs-17-HMR-vs-22LR-534x600.jpg
In other words, No do not shoot 17HMR in a 17 Bmag rifle.
No, this is 17hmr ammunition, not 17 Winchester super mag ammunition. Same diameter of bullet, different cartridges. Even if it would chamber, it would not operate properly.