I doubt that. Zimmerman is being found not-guilty, the reason why is irrelevant for the civil proceedings. His claim of self-defence may make it harder to win but it won't prevent Martin's family from filing just on general principle and to force him to cough up even more for legal fees.
FL. Stat. 776.032: “A person who uses force as permitted in s. 776.012, s. 776.013, or s. 776.031 is justified in using such force and is immune from criminal prosecution and civil action for the use of such force , unless the person against whom force was used is a law enforcement officer...”