On one hand, you seem to be asking if the wordpress.com stats plugin can be placed in your sidebar.
On the other, you state that your blog does not have widgets in which to place the wordpress.com stats plugin, assuming that this can be done.
I cannot answer those questions. What I can tell you is what I have done on my own wordpress.org blog. I have not activated the wordpress.com plugin.
All the free 3rd party stats counters that wordpress.com bloggers use can be placed in a text widget and then placed in the sidebar of your wordpress.org install.
I chose to do this with Sitemeter (ie. I put it in a text widget in my sidebar), rather than embedding it into the html on my wordpress.org blog.