Only if you apply a preview. Not inline while editing. That is how Markdown looks. Some editors will hide Markdown markup from,you while editing as a hybrid of editing and preview. Drafts is not one of those apps.
‘If you find that cluttered, consider using Markdowns reference style links where you place the actual resource address at the end of the document and you reference it by ID within the document.
On iPad and Mac, where multiple windows are support, you can open a separate preview window, which is updated with the HTML rendering of the Markdown as you make changes.
On iPhone (or also the other platforms) you can use preview actions, which display the rendering.