Deciding if I need to add a support beam in the middle or if it will be fine on its own.
According to Ikea, an Alex drawer bank cabinet is slightly over 14 inches wide. So 28 inches of the 96-inch desktop will be supported, leaving a 68-inch span open between the Alexes.
According to a shelf sag calculator website, https://woodbin.com/calcs/sagulator/, entering a 68-inch span of 24-inch-wide and 1-1/2-inch-thick birch, then entering a weight on the middle of the 'shelf' yields:
no weight, no sag
40 pounds in the middle, 1/8" sag
100 pounds in the middle, 1/4" sag
So how much sag depends on what gets put on the desk and where. If you don't plan to load the desk with more than a monitor, keyboard, mouse and elbows, there will be almost no visible sag.
An Alex is 27 1/2 inches tall, so there is room for an edge along the front and back of the desktop to stiffen the desktop if desired and still have 24-25 inches of vertical knee space. A 2 inch by 3/4 inch strip of suitable wood on edge attached as a facia on front and back will considerably stiffen against visible sagging. Even strips of 1 or 1-1/2 inch L-angle aluminum will help against visible sag.
Unless you're planning this desk to hold a lawyer's worth of law books, you should not need a separate center support.