When getting a breast reduction will there be fat pockets left on the sides (under the armpits)?

In general, no. Excess fat in this area is commonly treated with liposuction at the time of the breast reduction.

If you can "pinch an inch" or more in that area before the breast reduction is performed, then that "inch" will become more noticeable after the reduction because the breast is relatively smaller. I would ask your surgeon if he/she thinks that you might benefit from some form of liposuction at the same time as performing your breast reduction. Many times this helps to improve the overall appearance of the entire chest region by reducing the extra fat.