Make sure new FMC compatibility List
New FMC are you restoring the back from OLD FMC ?
1st questions , if I deregister from FMC at that time after deregister I guess still there will be no outage ?
There is no data disruption when you de-register from FMC.
Also I will re-resister from the new FMC and push the policy will it break the connection ? or there will be traffic impact ?
Re-register with FTD with new FMC, no breaking connection.
When you policy push - as long as you have moved OLD FMC backup to new FMC and all the policies are same and testing for the simple test policy that should work and not traffic impact.