Based on personal experience, it may smooth out some with use, but don't hold your breath. Actually, with use and familiarity, you may think that it smooths out but in actuality, it is nothing more than you not noticing the trigger as much. HK triggers seldom get better with use and if they do, it is marginal at best. That's why I recommend training through the grit. It will either work out or it won't. If it doesn't, cut your losses and move on to something that works better for you.
I have north of 5,000 rounds through my primary 45c with several thousand dry fires (I don't keep track of these) and my trigger in DA mode is just as crappy as the day it was purchased. The HK45c has the best SA trigger and reset, but the worst DA trigger pull of the HK family in my opinion. The only other HK that rivals the crappy DA trigger pull is my P2000SK. The DA triggers on my P30's and USPc are night and day better.