PHPmailer does not do anything special for character sets other than ISO-8859-1. It just encodes bytes in base64 or quoted-printable and adds some charset tags based on $this->CharSet set in email_to_user. I sometimes receive mail from PHPmailer including some garbled characters in Subject since it splits Subject into 75 byte chunks without knowing character boundaries.
Neither does (standard latin1) MySQL. It regards text in any character set as just a stream of bytes. It however works well with moodle because (I guess) moodle basically doesn't truncate or split text including multi-byte characters. The exception I experienced is text forms limiting maxlength but it may be browser's problem. Of course, moodle needs to know anyhow in what character set the text is stored. I can see garbled profiles stored in 'ja' when I set my preference lang to 'ja_utf8' because moodle can't guess the correct character set.
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(Off topic) Alternate character sets and phpmailer
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