When a microcontroller is in debug mode, does it freeze the entire MCU?
It depends on the MCU. Some (like TI's C2000 line) have a debug mode that allows the CPU to take interrupts while stepping through non-interrupt code. Timing and communication peripherals may have an option to continue working while the CPU is halted. But unless the documentation says otherwise or you've done some special configuration, you should assume that all peripheral activity will halt along with the CPU.