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My gut tells me that if there is any change it will be negligible. Yeah, we use mirrored blade tips for in hilt leds but in that case the light is pointed directly at the reflective surface. And for the amount of work necessary, probably not worth it. Is the tape conductive? If so, any contact with the small leads on the led, resistor, or FPC could be disastrous.

If you do test the theory, do it on a single pixel or small section of a strip.