Can I print an image from a separate content type in my page--front.tpl.php?
You can embed a view inside your front page template, insert this code in propper region. You'll need an image view

// Get the embeded view and render it.
drupal_render(views_embed_view('VIEW_NAME', 'DISPLAY_ID'));


replace VIEW-NAME and DISPLAY_ID with your data, you can find those values in last column on your image view