You can remove the Do Not Synchronize flag from all records without causing a problem, but there is a potential that doing so will cause duplicates in Luminate Online (which may be the expected/desired result).  Additionally, information that has been gathered since the implementation will sync to Luminate Online.

Depending on how much information this is, you might hit your API limit. You can call Salesforce to ask for a one-time increase to complete the sync; Salesforce may or may not charge you for the increase.