What PDF reader are you using? What tool are you using to select the image?
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In Acrobat, you can add a background image or color to all or individual pages that should not interfere with cursor clicks.
I'm using Adobe Reader X, ver. 10.1.16.13, and no tool selected. Open the PDF document. Using the mouse over blank areas, the cursor is the arrow icon, over text, it changes to the text entry icon. If I move the mouse over the image, in some areas, the cursor will change to a crosshair, and if I click then, the image may be selected.
While that works, I'd like to keep all the workflow within inDesign. If I were to use another program, I'd recreate the background in Photoshop, i.e. flatten the two layers and make it a single image.