Yes. Devices can be connected with USB in several modes. Only if USB debugging is working correctly then you will be able to connect the IDE (or Eclipse) to the device, not using B4A-Bridge. Basic4android uses ADB (a tool from Android SDK) to communicate with the device. So the problem is usually not in Basic4android.
Maybe in the future. You can choose compile & run and ignore the last message. In most cases developers are able to connect to a real device using one of the three methods: USB debugging, B4A-Bridge over wifi network or B4A-Bridge over bluetooth.
When I try compiling, B4A does not find the device even though it is connected by USB cable & USB Debugging is on (in my ZTE Blade phone): it doesn't matter whether USB Storage is switched on or not(in my phone). Interestingly, running 'adb devices' afterwards gives:
adb server is out of date. killing...
* daemon started successfully *
List of devices attached
CM7-Blade device
Could the above message about 'adb server' be connected with B4A not finding the device?
Thanks for the advice on ignoring the last message: I can transfer the .apk to the sdcard on my phone and install the app from there.