I just read this in the AsyncPro help:

"OnPortClose is generated when the serial port associated with the TApdComPort is physically closed.
"Setting the Open property to false does not close the associated serial port immediately. Buffers and structures need to be reset, and the physical hardware needs to be closed before the port can be considered closed. This event is generated when the physical port is actually closed and available to other processes." (my emphasis)

This seems to support my earlier suspicions.
It also suggests to me that waiting for the OnPortClose Event might be the way to synchronise it all & avoid problems?

I also read today that opening a port involves three Threads - not just the one that I speculated!