I have some thin rope border tiles that look really dull, but I notice when I wet them to scrub the left over grout out of the lines, they look really shiny and pretty. It made me wonder if I could coat them with some polyurethane to make them pop?
It's best not to put anything on ceramic tiles as they are non-absorbant. If you really want to try, buy a small container of stone Sealer Enhancer and brush it on a small area in an inconspicuous spot to see how it looks then how it holds up. By coating ceramic you're probably asking for maintenence problems in the future.
Not a good idea. It would not adhear well to ceramic tile and will change the color as poly is not perfectly clear.
Polyurethane would probably require a bond coat to insure permanent adhesion. In addition, it will yellow over time and may adversely affect the color. However there are some tile finishes that can provide a shine. Even car waxes might do the job. Look into something besides polyurethane.