Certainly the null byte can appear in utf-8; code points like \x2400, \x2500, . . . all have them

No, utf8 is specifically formulated to avoid null bytes in any codepoints apart from zero, eg

$ perl586 -MDevel::Peek -e'Dump "\x{2400}"'
SV = PV(0x8181f00) at 0x816e234
  REFCNT = 1
  FLAGS = (POK,READONLY,pPOK,UTF8)
  PV = 0x817c268 "\342\220\200"\0 [UTF8 "\x{2400}"]
  CUR = 3
  LEN = 4
[download]

That codepoint is represented by three bytes, none of which is zero.

Dave.