In general, no—but there are some exceptions.
As long as the camera arms are designed to compensate for the thickness of the soundproofing system, detection accuracy is not affected.
An exception is soundproofing systems such as the Winmau Wispa. These systems are specifically designed to absorb the impact of darts by converting the energy into movement rather than transferring it as resonance to the wall. As a result, the dartboard is mechanically decoupled from the wall.
Because the dartboard can move slightly during play, these systems may reduce detection accuracy.