subzali, off course it kept running, the alternator was supplying power at that point. It will not start, because there is no power from the battery to the ignition switch.
In other words, the large battery cable from the positive side of the battery goes down to the starter. It only provides power to the starter motor, that is it. The small fusible link wire is a two way street for power from the battery, or power from the alternator. When the engine is off, or the alternator is not functioning due to broken belt, internal failure, or voltage regulator issues, the battery will run the truck until it is dead. When starting, the battery is needed to trun the starter motor, provide power through the fusible link wire to the fuse block for the iginiton curcuit, which sends power to the coil and distributor and to the starter selonoid on the starter. The starter selonoid, activiates when you go to start, it makes two copper contacts on a shaft jump over and make energy flow into the starter motor from the large battery cable. The large battery cable does not provide any other power to the vehicle.
Once running, then the entire positive battery cable could in theory be pulled off, as the engine should continue to run on the alternator, or at least the fusible link wire. But I would not recommnd this, as it will affect grounding and such, and you could cause some funny problems with you charging curcuit.
Vehicles that just die if the fusilbe link burns up, have problems someplace that caused that kind of short, that extend beyond just a lack of juice from the battery. Something has shorted, the alternator is haywire, or the battery is dead.