Yes, as long as the agency determines that a formal conference is reasonably and logically related to carrying out its statutory responsibilities. 
 

No.  A no-cost contract is one where the contractor makes its money off fees the contractor collects and the government is not responsible for any costs.  A no-cost contract for an entire conference represents an improper augmentation of the Department’s appropriation.  Note, however, that fixed-price or cost-reimbursement contracts for conferences can contain certain no-cost elements.  See convenience fees.  A convenience fee is one that the attendee voluntarily pays to the contractor in order to obtain services such as meals, lodging and refreshments, that the Department the Department does not consider an integral part of the conference.  As such, the fees are not received “for the Government” but rather collected by the contractor for its own use.