No.
It’s a term used to describe rapid intensification of the storm which could result in stronger winds and increased snowfall because of the winds resulting form a steep pressure gradient.
It’s not about the intensity of the storm but about it’s development.
The “bombing” occurs when a low pressure system’s central pressure falls 24 millibars in 24 hours or less. The official term is explosive cyclogenesis, or bombogenesis which is actually really common. It can happen with any weather phenomenon, not just snow.
The term's use sounds more like a weather channel handwringer mechanism like thundersnow or like naming winter storms to up the anxiety factor. Next they'll be naming dust devils in Arizona.