It will in your Kimber... but then, that's the least of most Kimber issues. A total non-event with HK pistols.They are about .15 longer and I don't know if that impacts the feeding process.
Your preference for HST ammunition is well-founded. Its pretty much the best quality (and performance) "self-defense" commercial factory ammunition available today.
You might want to think about staying with the 124gr bullets. The 147s shoot rather high on common-issue HK sights at 25 yards; I have had five 9MM HKs- USPc, P2000, P30- and all shoot the 124s exact POA/POI. I actually carry the 124+Ps, which give a bit of extra velocity which is always good when having to shoot meat.
That said, the 147s work better (IMO) as a duty round for the po-lice, because the one defect of the 124 HST bullets is that they do NOT stay solid when shot through safety glass. This is because they are shorter than the others, and simply cannot be manufactured to ensure stability going through safety glass... which really shreds conventional projectiles.
All THAT said... as a retired LEO, I can carry pretty much anything I want to, and the 124 grain +P HSTs do pretty good against unprotected meat... which, as a "civilian" who will only shoot someone who is trying to hurt me or mine, is what I need.
FWIW, I know more than I should about all of this, because I work at a crime lab and examine bullets that come out of corpses and almost-corpses. The HST, along with the Speer Gold Dots, are the best I've seen in almost seven years of examining what we call "meat bullets". Much of what you'll see in gun magazines about "the best defensive ammo" is utter bull****.