Currently, no. These tags will not be rendered correctly. But the short answer is that they maybe should be.
The Markdown syntax documentation you reference is the general spec for the Markdown standard, not controlled by Trello or anyone by John Gruber, originator of Markdown. Here's the full quotation:
Markdown is not a replacement for HTML, or even close to it. Its syntax is very small, corresponding only to a very small subset of HTML tags. The idea is not to create a syntax that makes it easier to insert HTML tags. In my opinion, HTML tags are already easy to insert. The idea for Markdown is to make it easy to read, write, and edit prose. HTML is a publishing format; Markdown is a writing format. Thus, Markdown’s formatting syntax only addresses issues that can be conveyed in plain text.
For any markup that is not covered by Markdown’s syntax, you simply use HTML itself. There’s no need to preface it or delimit it to indicate that you’re switching from Markdown to HTML; you just use the tags.
The usage being referred to here is using Markdown to generate things like documentation pages, etc. We don't expect Trello to allow you to insert arbitrary HTML tags in the future.
A better benchmark of what you can expect Trello to support Markdown-wise is this site and the other StackExchange sites, which do
support other tags (
<strong>which</strong> <em>do</em> <s>support</s> <del>other</del> <strike>tags</strike> ).
I'll make sure to file a case with the Trello team to support these tags, if possible.