Add sidebar using a shortcode

Is there a way to include a sidebar in a page using a shortcode?

Basically, I have a site with a sidebar which needs to have the same content on each page (2 image links – I am using a plugin for this) and the sidebar needs to appear at the top right of the page – all pretty simple and standard so far……

…but on the home page I need the sidebar to appear a little way down the page (some of the editable page content needs to appear ABOVE the sidebar).

Basically, what I am thinking is if I use a page template to display the home page without a sidebar, I could then use a shortcode in the page content itself to place the sidebar wherever I need it (in this case, after the first couple of paragraphs and an image).

Something like…

[sidebar “primary-sidebar”]

…would be ideal!

But… is this possible?!

Thanks for any help ??