Can A Cracked Thermostat Housing Cause Smoke

Today I found out my thermostat housing has a crack in it, im sure it was worse but now its bad. It drains my coolant fast and pretty sure heats my car up. I want to know if a leak in the housing can cause white smoke from the tail pipe? What will it cause if not that?
I heard about a head gasket before but theres no oil leakage and no oil in my coolant or water in my oil. Im so confused
98 eclipse rs

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