No, the accessory 45-70 BC barrel comes sightless, you can order the front sight with it, but it may not be the one you'll want, they put one of two 17A sights on the BC, a .494" or .584", the .584" is too tall, the .494" works, but the .404" works best as far as many are concerned here, they don't offer it. They offer 3 rear sights, the William WGRS, and 2 different FP sights, one with target knobs, you probably won't find a better price on any of the Williams sights that at H&R. If you're gonna scope it, you'll need to order a scope base.
The Colt Carbine comes with a ramp rear sight, but it is drilled and tapped for a scope base or the WGRS sight. You could have the 20" Colt barrel fitted to a Handi frame, there's no difference in the BC or Handi frames, they're all SB2 frames. I wouldn't be concerned about 45 Colt recoil, compared to the 45-70 or 500 S&W, it's a lightweight.
The only 7mm barrels currently offered are the 22" 7mm-08 and 26" .280 Remington, they have in the past made Handis in 7x57 and 7x64, but finding one of those used is as rare as hens teeth.
Ya can't have too many Handis, many of us here have a bunch, not just barrels, but complete rifles, there's always room for more!!

Tim