Can an employer who uses a bi-weekly pay period pay its employees overtime pay for working in excess of 80 hours per pay period rather than for over 40 hours per week?

No.  In calculating overtime pay, the number of hours worked each week in the pay period must stand-alone. If an employee worked 35 hours one week and 45 hours the second week of a pay period, the employee would be due 5 hours of overtime-premium pay for that pay period.