Does a specific leech work before/after conversion?

Suppose I have 100% Cold to Fire with some cold spell.

Do both the modifiers "1% cold damage leeched as life" and "1% of fire damage leeched as life" work?

Or does it need to damage first, meaning that cold damage leech would no longer function.

Leech is an on-hit effect that applies based off the actual damage dealt. Only fire leech works in that scenario.