Just discovered something interesting:
From what I read, normally when you plug the cc2650stk into the cc-devpack-debug without a battery and attach the combination via USB, the debugger identifies as a "Tiva Device Firmware Update" USB device (i.e. it is in DFU mode) and can't be used to flash the cc2650stk, This is what mine does at least.
However, by using xdsdfu tool included with the "XDS Emulation Software Package" (see http://processors.wiki.ti.com/index.php/XDS_Emulation_Software_Package - the tool is in the "ccs_base\common\uscif\xds110" subfolder) I'm able switch the debugger back to runtime mode with the command:
xdsdfu.exe -m -r
Yes, this is a hack, but it has the side effect of switching from DFU to runtime mode. Then the debugger will work to flash device as normal as it will now identify as a "XDS110 with CMSIS-DAP" and I can program and use the cc2650stk, all WITHOUT ever using a battery or even plugging or unplugging the SensorTag. Note, that executing the above command again will put it back into DFU mode.
My cc-devpack-debug is version 1.2.0 the Sensortag cc2650stk is version 1.1.3. I'm using the SmartRF Flash Programmer 2. I did have to update the cc-devpack-debug firmware as described in the post Unable to connect CC2650 Sensor Tag via XDS110.
I would be interested if this works for anyone else :)