@poeml following up myself, using an external, powered USB hub indeed fixed the problem. The USB adapter is now correctly usable after system bootup. (I use the official Raspberry Foundation hub, which promises to avoid issues with backpowering.)

@poeml more precisely, the Nano's FTDI chip connects to the booting Raspberry, but instead of registering a single device there are 4 (!) log lines claiming registering 4 devices (very funny), and none of the devices are bound.

May 23 23:16:21 bramble kernel: [    3.738087] usb 1-1.5: new full-speed USB device number 5 using dwc_otg
May 23 23:16:21 bramble kernel: [    4.283520] usb 1-1.5: new full-speed USB device number 6 using dwc_otg
May 23 23:16:21 bramble kernel: [    4.768136] usb 1-1.5: new full-speed USB device number 7 using dwc_otg
May 23 23:16:21 bramble kernel: [    5.268161] usb 1-1.5: new full-speed USB device number 8 using dwc_otg

I don't find a way to trigger re-registering the device, or power-cycle the USB port, via software. I can only power-cycle the whole USB bridge, which means that the LED goes out (the Ethernet chip is switched off as well...) and LED goes on again, but with the same faulty registering as when booting.

 # cat reset-usb
#!/bin/bash
echo 0 > /sys/bus/usb/devices/1-1/authorized
sleep 1
echo 1 > /sys/bus/usb/devices/1-1/authorized

Unplugging and replugging always works.

For the record: Raspberry Pi version 2 with the 4 USB ports, just updated to Debian 8.0 (Jessie). I didn't check with Debian Wheezy if it worked then. The Nano was linked from MySensors store I believe and works great otherwise. I have two of them and both have the same problem (or the Raspi's USB stack has the problem, who knows).

@guzzler I stumbled over the same issue. The FTDI chip on my Nano is correctly recognized as USB device when I attach it to the Raspi. However, when I reboot the Raspi, the device is not there. I need to unplug and replug it.

That's not normal behaviour of an USB device. And it's quite hindering deploying the Nano as gateway via USB-serial. Maybe it has something to do with automatically performed reset on the Arduino Nano board??

(The hint about attaching directly to serial is great. Noted for later.)