There might be room. After all, our hypothetical spy is apparently well-used to storing things there. 
But my point was that duct tape is only water resistant. Not waterproof, even if it IS shiny. Placing it in an environment that is close to 40C constantly and is completely m0ist (even before you consider the considerable amount of lube to insert the thing) is not conducive to having the tape adhere for any length of time. At the very least, fluid is going to migrate under the edges of the tape.
Edit: apparently m0ist is a bad word here…
