When using the "Add quote items to contract" feature to sync services to an existing PSA contract, there is currently no option to set an effective date. The service is added using the contract's original start date (e.g., Jul-01-2020), rather than a current or user-defined date. This applies to Autotask, ConnectWise and HaloPSA in the same way: all three receive the contract's start date as the effective date of the new lines.
For new contracts created in Salesbuildr, an effective date can be set before syncing. This same capability should be available when adding items to existing contracts, for all three PSAs.