Thundersnow does indeed meant that there will usually be more snow.
Whenever it's snowing and it's thundering during that snowfall then you can usually expect a lot more snow to follow and even a blizzard or other major snowstorm could be on it's way.
Thundersnow also produces about 2 to 4 inches of snowfall per hour which can easily pile up so if you're getting thundersnow it's best to stay off the roads because it's likely that a major snow storm is coming after the thundersnow.
When Thundersnow occurs it is often a part of a severe winter storm or blizzard.