I did some tests, and this is what I experienced:
Wikicode / wiki markup will work on wiki pages such as profile pages, free space pages, category pages, etc.
Because comments are posted on wiki pages, templates will work in comments. Bracketed tags (such as <ref> and <nowiki>) are disabled for comments.
Bracketed tags are entirely stripped from private messages. Because private messages aren't part of a wiki page, the templates don't work.
If a private message is sent with a comment that includes a template, the bracketed tags included in the template are stripped, so you will just see the text of the template.
G2G is an entirely different software than the wiki part of WikiTree, so wiki markup does not work.