I noticed in some product descriptions at AdaFruit.com the following:
“The RTS pin (as of Arduino IDE v18 this will work perfectly for uploading to ‘inos)”
More experimentation is needed to determine which versions of AVRdude will twiddle the RTS pin. But it appears that an FTDI cable (like this one: https://www.adafruit.com/product/70) should work for automatically resetting the microcontroller when bootloading, without any need to modify the cable.
Regardless the experimental results, I will change the schematics to allow either the RTS or DTI pin out of the FT232R to be connected to the reset line through a 0.1 uF capacitor.
[Update 25 May 2017: AVRdude version 6.3 has been tested and shown to reset the processor using the RTS pin. So no modifications to the FTDI cable are required: a 0.1 uF capacitor from pin 6 of that cable to the RESET line will allow AVRdude to automatically reset the processor prior to bootloading.]