To answer the question, yes, Delta allows employees to sit in first class. The priority goes Medallion upgrades, then paid upgrades, then deadheading crewmembers, then personal travel (non revs) according to seniority and priority.

They don't generally grab Joe Six Pack and offer him a first class seat just to fill the front. That would diminish the value of the product. They'd rather let employees sit there if the seats will be empty anyhow, which is a nice perk.