Christine,
Sync will naturally fail as these are required fields in SFDC as you mentioned. However, unless you're using Marketo Program > SFDC Campaign sync, you'd need a program with either the "Sync lead to SFDC" or "Add to SFDC Campaign" flow step to sync leads - they are not synced automatically. To block sync, you could simply create a smart list that holds anyone missing the key information, and add a choice on the sync flow step to block folks on the smart list.