Am I to assume that elements 0-69 and 71-120 are undefined?

Yes. If they were undefined, they will remain undefined.

$ perl -le'
    my @a;
    print 0+@a;
    print defined($a[0]) || 0;
    $a[70] = "a";
    print 0+@a;
    print defined($a[0]) || 0;
'
0    0 elements in the array
0        and the first one isn't defined.
71   71 elements in the array
0        and the first one still isn't defined.
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My problem is that not defined ($array[$number] returns false

Then $array[$number] is defined. It was given a value somewhere else, possibly through autovivification.

$ perl -le'
    my @a;
    print defined($a[0]) || 0;
    $a[0][0];
    print defined($a[0]) || 0;
'
0
1
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[@{$x->[3]}>0 gives] Can't use an undefined value as an ARRAY reference

Then $array[$number][3] is not defined.

Update: Added code blocks.