So is it possible for the ++ operator to increment a value that cannot be seen in numeric context?

Numerical context refers to the conversion of an operand's value to a number by operators that work on numbers. Perl can get a number from any value. The process might result in a warning and the result might be useless, but it will always end up with a number. That means there is no value that cannot be seen in numeric context. That means your question doesn't make sense.

On a side note, "++" handles strings differently than other values.

>perl -wle"$a='a'; print $a+=1"
Argument "a" isn't numeric in addition (+) at -e line 1.
1

>perl -le"$a='a'; print ++$a"
b
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