As the PICAXE chips are single core, multi-tasking is in effect a time-slice process where one command in each task is processed before stepping to the next task in a round-robin method.
Some commands totally block the rotation between tasks (eg SERIN) while other commands (eg PAUSE) allow the processing to move immediately on to the next task.
For the tune command, to maintain consistency of the tune, the processor core must keep generating the tone/note.
Think of how the interrupt system functions where inputs are “checked between execution of each command line in the program, between each note of a tune command, and continuously during any pause command”.
You would tentatively be able to step to the next task at the end of a note but the likelihood is that there may be extended pauses between two notes within a single task.
Your question likely needs either you to “try and see” what happens or a clarification from Technical or hippy.