I achieved something very similar using only a header widget and custom CSS. Look at my site.
Here is the custom CSS, which controls the positioning of the header widget:
.header-widget {
position:fixed;
top:10px;
left:10px;
}
Then, enable the header widget, drag a text box onto it in the widget panel, and paste your adsense code into it. Save, and then view your site. It should be there.
All done with no child theme, and no digging into PHP. It works! Try it!
Ken