yes. absolutely. there are some instances that may require them to go to a closed door, confidential, meeting to discuss items that are sensitive. after the board discusses those sensitive items they usually open up again to a general meeting and may share the results of the closed door session without sharing who said what.
The board is allowed to go from a regular meeting session to an executive meeting session and then resume with the initial meeting. However, this will depend on the confidentiality of the topic they are discussing and the company's or organization's policy. In most cases, meetings should be conducted without interruptions.