But what I haven't quite figured out is *why* ^_#ALPHA wouldn't match on 'ALPHA, I AM'. Is it because the character class has to match _some_ character?

Yes -- it has to match exactly one character ... you can, however, use the quantifiers:

/[A]B/;     # must be 'AB'
/[A]?B/;    # 0 or 1, so 'AB' or 'B' or 'CB'
/[A]+B/;    # 1 or more, so 'AB', or 'AAAB'
/[A]*B/;    # 0 or more, so AB' or 'AAAB' or 'B' or 'CB'
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My train of thought was that the negation would be primary. "Is there an underscore or a hash leading?" "No."

"Is there a character that is (NOT) an underscore or a hash"
The "NOT" being there iff there's the leading carat.