probably.
http://www.technoglowproducts.com/glow-in-the-dark-paint/ Their paint is UV reactive.
You could consider glass beading the polycarbonate to get the paint to stick or use matt polycarbonate.
You do want the water to see the UV-C light/
http://www.company7.com/library/c7_uv_primer.html
painting polycarbonate - not sure what to expect. if you can find a UV transmittive primer, you might have a better chance, Rough the surface, always helps. glass bead or whatever media is appropriate or sandpaper.
Thick plastics cut well with carbide table saw blade. You might have better luck with thinner stuff running the blade reversed or try a laminate blade.
Painting is an art that I have mastered and surface prep plays a big role.
I've bent acrylic, but not polycarbonate.
I've drilled 5/8" holes in both acrylic by grinding my own bit, similar to a pilot point or bullet bit style. I usually worked with 1/4" thick. 5/8" is a pretty big hole.
The application was a hood/shield where panels were held on with 5/8" wingnuts and held by handles. One panel was about 3' x 8'. We initially used acrylic until we had an explosion. We then changed to polycarbonate.
Dishwashing detergent and a little water in a spray bottle works as a lubricant.
You can fire polish the edges. Edge joining, I personally have no experience with.
I have glass blowing experience (lab stuff, not pretty stuff) too: both quartz and borosilicate. Add welding, soldering and brazing I have most operations covered. I did sealing under vacuum with mosty quartz using a Hydrogen/Oxygen flame. the borosilicate glass propane/oxygen.