Adding the gadget
Go to Design, Page elements. Click Add a Gadget (any link will do, we will move the gadget to proper place afterwards).
Write the text/html you want in your "sticky post", click Save. I suggest to not use any title, it helps the correct alignment when gadget is hidden.
Now drag the new gadget to top of blog posts, like this:
Save.
Hide the gadget on other pages than first
Open template html for editing. Before </head> add this:
<b:if cond='data:blog.url != data:blog.homepageUrl'> <style type='text/css'> div.main div.widget.HTML .widget-content { display:none; } div.main div.widget.HTML { margin-bottom:-30px; visibility: hidden;} </style> </b:if>
Depending on your template you might have to change the value -30px to adjust the position of blog texts. -30px works for "Simple" template.
How to mimic a post in gadget html
Here's a "template" you can use in HTML/Javascript gadget contents to make the gadget have post-like title, spacing and body text.
This template works at least in "Simple" and "Awesome Inc." templates, probably in others, too. :)