The H/NH really only matters in the top-tier residencies where they rely on minutiae to differentiate a slew of applicants who are all very competitive (and thus very homogeneous). If you aren't up to the level of the other applicants (who got H/NH's) that works against you for those highly coveted spots.
For the majority of residencies, not so much. But its always good to inquire to the program director at whatever field you're considering at your school, because different specialties have widely divergent things they look for in applicants. Some consider research a necessity, others want to see good clinical grades, others good board scores, etc.
Either way, it's good practice to always try to shoot for those levels just to make sure you master the material, because there IS a rough correlation between how you do in your BS classes and how well you do on the boards (and yes, I know there are plenty of anecdotes to the contrary, I said rough correlation). There's a slippery slope phenomenon with some who "shoot" just to pass. Some manage it just fine, others are at risk of failing a class or two. And failing a class WILL hurt you for residency if you don't make it past remediation and have to repeat a year. But don't tear yourself up and think you're sacrificing your future if you end up amassing mostly P's. In the grand scheme of things, any deficiencies in your BS grades can be readily overcome by good board scores/clinical grades/LORs for the vast majority of programs.
