The experiment you propose seems fairly sound, but you would need to test it many times to check whether a consistent co-efficient of friction can describe a beetle's stickyness well. With small creatures, friction is often way too blunt a concept to measure or describe a their ability to cling to a surface. Some creatures can switch their clinging ability on or off at will, by forming temporary van der Waals bonds with the surface although I'm not sure whether any coleoptera (the beetle order: aptly named the "sheathed wings") can do this: you'd either need to ask an entymologist or try the experiment to see. Mostly creatures who do this have small hairs on their feet to exploit van der Waals forces for attachment, and some can switch between an effective infinite co-efficient of friction (i.e. you can't unstick the creature without ripping it apart) and zero co-efficient almost instantly. Actually, this is not friction at all since the reaction force from the surface is towards the surface and the creature's presence upside down on the surface puts the surface is a state of tensile rather than compressive stress, as in a friction scenario. The geckos are the most famous users of the van der Waal force to afford an at-will, dynamic sticking ability and their sticking organs (kitted with nanometer scale special hairs called setae) can be seen in the photo below (source: Wikipedia "Gecko" article). But there are also many arthropods who can do this as well: flies and spiders come to mind.
Moreover, in physics when you get down to insect size and smaller, often everyday physical intuitions don't work so well. The importance of "cold welding" type phenomena and van der Waals forces for very light, small things makes friction nonuseful for the description of small being statics.