Capturing timer value based on external interrupt , leveraging the 62.5nsec (16MHz) resolution) of the ATMEGA328 on the Arduino Uno

You can, but you probably shouldn't. Everything will be fine until the output buffer fills up.

When the buffer is full and interrupts are disabled (as they are in an ISR), the serial output goes from interrupt-driven to polling. It will wait ages for the hardware buffer to be available and then move one character out of the software buffer. That will make room for another character of your output. It repeats the waiting until the last of your characters reaches the buffer.

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