Yes, "damage to the land" checks are affected by modifiers to the land's health. For example, the Kingdom of Sweden's Level 1 Heavy Mining effect means they would need, e.g., 5 Damage to add Blight if the land has only 1 Health due to "All Things Weaken," but 14 Damage to add 2 Blight in a land with Vital Strength of the Earth {Resilience}'s Sacred Site.

 

The same applies for the Habsburg Monarchy (Livestock Colony)'s extra loss condition (which would need 7 Damage in a 1-Health land to count Blight and 16 Damage in such a Sacred Site to count Blight).

 

Some Events affect the land's health, such as "The Land's Bounty Exhausted" or "Depleted Soil".