Fan belt

Is it safe to drive 1 mile to a repair shop without a fan belt or if it breaks in transit on a 2000 Honda Civic?

It’s not really a fan belt; more of an accessory belt.
You could make it IF the battery is fully charged and IF you don’t get caught in traffic.

Many years ago one could drive a car across an entire state on the battery alone. Modern cars have a tendency to stall out once the battery voltage drops too low; and they can drop quick because of the electrical load placed on the system by the fuel pump, fuel injection/emissions equipment, and whatnot.

One mile is doable. Get caught sitting in traffic for time eternal and it may not be.