No... wp.com users cannot add/edit the HTML (or in this case the PHP) files. I'll try to explain as best as I can.
You know, when you add a photo to your post, you click the media button, upload the image to your blog (or link it from another URL) then you click the "insert into post", right?
Well, after doing that, you would switch to the HTML Editor, like it's explained here:
Then you will see the HTML code that's behind your post. After switching to the HTML editor, you would need to replace the existing HTML for the image that you just added with the code I provided; of course, you would need to make the necessary changes so that your image is displayed. Basically, the only things you would need to change in the inline CSS are the values of the "background" property as well as the "width" and "height" properties. Those would be the bits in capital letters:
<img style="background: transparent url(YOUR-IMG-URL) 0 0 no-repeat; border: 0; height: IMG-HEIGHT; margin: 0 auto; padding: 0; width: IMG-WIDTH;" src="http://tfockler60.files.wordpress.com/YEAR/MONTH/nothing.gif" alt="Helghan Soldier" title="Helghan Soldier" width="IMG-WIDTH" height="IMG-HEIGHT" />
You would also have to upload the "nothing.gif" to your blog and point to it as shown in the example above (that's why I put YEAR and MONTH in caps because those will be different in your case).
You'd have to repeat this process with every image you want to post (however, you won't have to upload "nothing.gif" everytime you want to do this because you can always point to the same image).
The drawback is that it can be a laborious task if you have LOTS of images...
I hope this clarified the process better?