Yes, the chrome lining is much harder than bronze bristles. You cannot hurt the bore with it. The only way you can damage the bore is with aggressive over cleaning and dirt particles trapped between the bore and bristles. Use lots of patches and solvents in between scrubs to reduce the particles.
I prefer the RemClean method where the bristles are wrapped by a patch, Cleans copper and carbon easier and faster than the bristle method.
I've seen bores wore out at the muzzle due to the rod rubbing hard on it and not straight. I recommend a muzzle guard.
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Back to barrel life, after 5,000rds accuracy will start to deteriorate, but it will keep shooting on to 10,000 easy. Since that barrel will not be a serious match contender, I wouldn't concern myself until it won't hit the broadside of a barn.