Jojo,
It depends. 7.62 and .30-06 brass from Lake City have crimps that will damage a primer, as MetalGod described. However, on .223 the crimps seem to be less robust, and I have, like you, accidentally primed some I thought had gone through my swager, but hadn't. The fact is, they primed easily enough that I didn't even notice until about the fifth one, for which the extra effort was a little more noticeable. It seems the thinner crimp had largely been ironed out when I pushed the original spent primer out, and that just doesn't happen much with larger crimped primer pockets. So if they went in with reasonable effort, and the primer cups don't look flattened and are below flush with the case head (for an AR) they probably will shoot fine.
One thing to watch with Lake City is that the primer pockets are drill and the drill sometimes walk a little off center. They're not as bad as Fiocci cases, but I've had a few over time that were off center enough to break a decapping pin.