Sure it's possible. Different markup languages have different levels of features: some like Markdown only very basic elements, some like asciidoc, orgmode, docbook, html, more differrentiated. There's 3 approaches converting from complexer to simpler formats:

• lossless aproach: only convert the supported parts (e.g, dump everything in the output, converted or not)
• lossy approach: extract the supported parts (discharge everything unsupported)
• convenient approach: convert the unsupported parts to a similiar element (definition list to - list, figure + figcaption to ![]() *caption*, stuff like that)

I know of Typora doing a good job with the convenient approach, though still partially lossless.

Sylpheed (E-Mail client) does a good job at the lossy approach, for plain text display of html.

pandoc does the lossless approach well. But it laso depends on which of the multitude of markdown outputs you've picked.

edit: Could Voyager please stop sanitizing markdown image links in inline code?!