No, the clicking you hear when turn on the turn signal is a mechanical sound, usually anyway. it is the opening and closing of a circuit similar to a light switch. In many vehicles this was controlled by a relay that could be swapped out for one that is designed for the low LED load rating. The hyperflashing is a safety mechanism that is designed in to alert the driver when the bulb isn't pulling enough current, thus the lower current LEDs activate this safety feature.
As far as I'm aware, the only thing that can be done is add in a resistor into the circuit. It's one reason many of us here don't switch to LED turn signals. By adding that resistor you loose the hyperflash safety feature. Some bulbs will actually come with the resistor.
I gave up on turn signal LEDs, too much of a pain in the butt, and not actually much brighter.
I'm curious what turn signals you installed. just the bulb or a full kit?