Yes you should, and it should be fairly easy:
If Elite recognises the HOTAS on its own, then when you press a button to assign a command on the in-game options bit, it will come up as Button 1, Button 2, etc...
Then all you need do is hold down whichever button combination you want to create the 'double-down' function and there you go. It should assign the commans as something like [Button 1]+[Button 12]...
If it doesn't do this automatically, you should still be able to assign buttons to SHIFT, ALT, CTRL, etc in the HOTAS's own software.
I do the exact same thing on my CH kit - I have three buttons under my fingers on the throttle, which I use excludively as shift functions - Holding one of those down, I then get four extra controls on the cross-hat. Hold the next button I get four more from the same hat, and so on. Basically a single 4-way hat ends up offering 16 functions. Multiply that up and my basic 35 controls becomes 140!!
Also look around to see if your HOTAS has some kind of map that you can use to record and remember which commands you put where - Summat like this:
http://i.imgur.com/zz9JBo6.jpg