The Sig .40 S&W to 9mm conversion takes more than just a barrel (unlike the .40 S&W to .357 Sig conversion). The kits that Sig sells (slide, barrel, and magazine) work quite well but since they are Sigs they are pricey.
This is true for factory 9mm barrels. However, I think what the OP is talking about is a 9mm conversion barrel
like ones offered by Bar-Sto and EFK Firedragon. These 9mm conversion barrels are designed with a larger outside diameter so that they will fit into a .40/.357 frame. They are either semi-drop-in (Bar-Sto's words - 70% will drop in and fit) or match grade (have to be fitted by a gunsmith).
I have a Bar-Sto 9mm semi-drop-in conversion barrel for my .40 P229 and it has been 100% reliable and accurate using .40 mags and recoil spring. Some users have chosen to replace the recoil spring with a 9mm one and used 9mm mags because there have been reports the .40 mags may not feed reliably when fully loaded.
I use my conversion only for cheap range practice so I have never considered using it for CCW. Logically, I can't see why it couldn't be used for carry, especially if the barrel has been fitted and 9mm mags and recoil springs used. However, mentally, I might feel some doubt about reliability just because the gun didn't come that way from the factory. I guess the one concern would be the extractor.