Hard for most of us 2-cycle sprint racers to say. Most organizations spec a tire so you don’t have the option to try different compounds.
Testing different compounds would be the only way to tell for sure.
When you’ve exhausted all possible tuning combinations to free the kart up properly on a tire and you still are struggling to get it free, then a harder tire might benefit you.
I would think there would be SOME setup that would free the kart up to make the tires work properly, unless we are talking really low hp stuff. I feel like even in Yamaha you could get the kart rolling nice through the corners on a super soft tire. My note about straight line speed being compromised by the extra rolling resistance of the tire still stands though.