Yes is can in the short term, cremation ashes contain calcium and calcium phosphate these chemicals acts like salt and draws the water out of the tissue of the plant leaf.
This will happen if not thinly spread, it acts like a fertiliser also impacting the nutrient balance within the soil.
The less the ashes spread and the greater the sensitivity of the grass the more the impact.
Groundsmen and women at golf courses often bemoan people scattering loved ones ashes on a green. As do the Ben Nevis Partnership who have noted the ecology of the mountain top has been impacted through repeated scatterings.
However if it is a one-off, thinly spread and watered-in or in rainy period the lawn is unlikely to be impacted or if it is, it will very soon recover.