Not on its own, and we would rather say that plainly than sell you a fix that does not hold.
Restoring blocked intake venting addresses one contributing cause — an attic that cannot ventilate runs warmer than the roof above it, which is part of what drives the melt-and-refreeze cycle. So it genuinely helps, and on some houses it helps a lot.
But ice dams are usually a combination of three things: ventilation, insulation depth, and air sealing between the living space and the attic. If warm air is leaking up through ceiling penetrations, or the insulation is thin, opening the soffit vents will improve matters without solving them. Anyone who tells you new soffit alone guarantees no more ice dams is overselling it.