It is certainly feasible. But both are fuses. The fusible link has the property of being more forgiving for transient overloads than regular fuses so that is why they got used as a main fuse. Wait a minute... the car chase in Bullitt is starting......
I keep hoping the Charger survives.....Oh well; that's Hollywood for you!
The 2 big bangs was probably the electrical system failing and the ignition cutting in and out as it failed; the bangs were a result of the ignition stopping, gasoline building in the exhaust for a moment, and then lighting off when the ignition fired up again a couple of time before it fully failed.
Do this to check for a short in the system:
Get a regular 100W incandescent light blub and get ready to connect it in series with the battery - lead to ground. With the doors closed and everything off, connect an 14 or 12 ga wire where the fusible link was installed. Connect up the light bulb; if you have a short in the electrical system, the light will glow but the bulb's resistance will keep the current low. If you get this glow, remove the bulb, then disconnect the 2 firewall plugs where the fusible link does NOT connect through and re-connect the bulb to see if the bulb still glows. If it does, the short is in the inside harness. (You can hook the bulb directly across the battery at the start to see how much the glow will be from a dead short.)
BTW, fusible links do fatigue and go out so that may be your only issue.
BTW#2; the wire on cars is small in those days because it was a cost thing. Copper in cars carries current no better or worse than in houses. But house wiring is set by the NEC (National Electrical Code) and has conservative factors involved since people burn to death due to bad house wiring. The consequences of failed car electronic is rarely as bad and there are no set standards, just cost and reliability tradeoffs.