True it is, but you wouldn't connect two transistors like that for this use, it's a VERY poor way of doing it - you would feed the first collector from a much higher voltage, with a current limiting resistor. The conventional darlington (as you drew) drops far too much voltage across it because the two collectors are joined together, it also seriously reduces the gain if you use it as a switch.
For this requirement (very high gain) I would probably use three transistors, with the middle one a PNP.