The bracket and the five ton cable that encircles the upper control arm cross shaft is GM's answer to Ralph Nader's instigated safety recall and law suit resulting from broken motor mounts. (do not loose those parts as they are very valuable do to rarity today). That strap limits the motor's movement when the motor mount breaks. It will not work with tubular steel headers as it relies upon the structural strength of the cast iron manifold to hold the bracket in place. The reason those parts are so rare today is everyone that installed aftermarket headers threw those parts away. They were installed on every Chevy made after 1958 that was brought into their local dealership to get the cable installed for free, because of the first federally mandated product safety recall in history.
If you go to tubular headers you will need to replace your simple vulcanized rubber (glued together) motor mounts for a 1958-'68 year car (you want the short and wide and not the tall and narrow size used on newer cars from 1969-'72.
The dimensional size of the motor mount changed in 1969 and up through 1972. Most parts stores not only stock the newer style, but they will try and hand it to you if you ask for a SBC motor mount because the computer says it fits: they will not fit on your car as you need the older style mount. You want a one that is interlocking; so ask for one off of a 1966 360 horsepower 327 SBC Corvette engine to get the correct tall short and wide sized part the first time out. (measures 2-5/8th inch between the tangs and the hole in the tang is 1-3/4 inch from the block's mounting surface).
Headers make a big performance boost and they do so by restoring lost horsepower caused by the cast iron manifold allowing one cylinder to bleed exhaust gasses into an adjacent cylinder polluting the fuel air charge with spent gases (works just like an EGR valve). That one polluted cylinder yields most of the 25 to 30 horse gain caused by bolting on headers.
Where headers cause issues is in installing an alternator on an older car without accessory mounting holes machined into the heads (1968 and up). The older 1958-'68 Chevy used longer brackets that allowed the V-belt to fly off at high RPM. To fix this issue Chevy went to the long water pump in 1969 and brought the accessories in closer to the motor (used shorter V-belts) with all new accessory brackets that bolted to the cylinder heads.
As noted the older cars require the aftermarket bracket to mount the alternator relying on a stamped steel part that he had to bend to get it to fit. Unfortunately the stress on the alternator will easily bend that bracket out of alignment again unless reinforced (gusseted).