Can I automate tar's multi-volume-feature?

Here is a solution:

printf 'n file-%02d.tar\n' {2..100} | 
    tar -ML 716800 -cf file-01.tar Documents/ 2>/dev/null

where 100 is a number greater or equal to the number of volumes.

Edit

Setting a big number should not be a problem, though I tend to not take a ridiculous one.

An alternative could be a "next volume" script, that you can set with the -F option,

tar -ML 716800 -F './myscript file' -cf file.tar Documents/ 2>/dev/null

then in ./myscript put

#!/bin/bash

prefix="$1"
n=1
while [[ -e "$prefix-$n.tar" ]]; do
  ((n++))
done
mv "$prefix.tar" "$prefix-$n.tar"
echo "$prefix-$n.tar"

It will be executed at each volume end, and will move file.tar to the appropriate fileNNN.tar. For the last volume the script will not be executed, so the last volume name stay file.tar.

Edit 2

I ended up with the following elaborated solution.
Here are two script, one for the creation and the other for the extraction:

#!/bin/bash
# CREATION SCRIPT

# save on file the initial volume number
echo 1 >number

# multi-volume archive creation
tar -ML 100000 -F './tar-multi-volume-script c file' -cf file.tar Documents2/ 2>&-

# execute the "change-volume" script a last time
./tar-multi-volume-script c file

and

#!/bin/bash
# EXTRACTION SCRIPT

# save on file the initial volume number
echo 1 >number

# execute the "change-volume" script a first time
./tar-multi-volume-script x file

# multi-volume archive extraction
tar -M -F './tar-multi-volume-script x file' -xf file.tar 2>&-

# remove a spurious file
rm file.tar

where ./tar-multi-volume-script is given by

#!/bin/bash
# TAR INVOKED SCRIPT

mode="$1"
prefix="$2"
n=$(<number)

case $mode in
  c) mv "$prefix.tar"    "$prefix-$n.tar" ;;
  x) cp "$prefix-$n.tar" "$prefix.tar"    ;;
esac

echo $((n+1)) >number

Obviously you have to change many bits here and there to adapt to your situation and to be sure it would work in cron, that is always a little challenge.