I want to know whether a numeric \x escape can be used to represent a character with a codepoint from U+0080 to U+00ff within a regular-expression character class.

Yes, you can. \x80, \x{0080}, \0200, \N{U+0080}, etc all work. You could easily have ascertained that yourself.

$ perl -E'say "\x80" =~ /^\x80\z/ ?"match":"no match"'
match
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Elsewhere, you've asked the same question but under use encoding 'UTF-8'. The UTF-8 encoding of U+0080 is C2 80, so...

...well, I can't find a way of matching U+0080 with \x or \0, but \N works.

$ perl -E'
    use encoding "UTF-8";
    say "\xC2\x80" =~ /^\N{U+0080}\z/ ?"match":"no match"
'
match
[download]

Of course, placing the literal character in the regex pattern works too. You can insert it into the source code, or interpolate it in.

$ perl -E'
    use encoding "UTF-8";
    $x = "\xC2\x80";
    say $x =~ /^\Q$x\E\z/ ?"match":"no match"
'
match
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This is a known limitation because the documentation shows a workaround for similar operator tr///. tr/// needs a workaround because it doesn't allow interpolation.