Yes, if a quorum is present. According to Robert’s Rules of Order Newly Revised (commonly called “Robert’s Rules”), regular meetings mean the “periodic business meetings” of an organization so it would follow that the business portion is necessary. However, members could decide to shorten a particular meeting by general consent or by a specific motion on the day of the meeting. Under general consent the presiding officer would call the meeting to order and then say something like “If there is no objection, we will dispense with the business meeting today and adjourn.”
If the meeting section of your bylaws includes a clause which reads something like “…unless otherwise ordered by the membership or the board of directors,” the membership/board of directors could vote to dispense with a business meeting that is scheduled for a particular date. For example, if a regular meeting is scheduled for March 2016, you could vote not to have the business meeting that day, but you could not vote to dispense with all March meetings except by changing the bylaws.