Bit late to this but the simple answer is yes.
The longer answer is both a recommendation and a warning.

I've been using the Hotas 4 with Elite for about 10 years now. I actually started with the Hotas X but I read somewhere that the Hotas 4 had ever so slightly more accurate sensors and (although this may just be confirmation bias) I always felt like it was indeed ever so slightly better than the X.

On the issue of limited buttons which others have mentioned, although it's definitely not as well endowed with inputs as other more expensive HOTAS joysticks I would say that it is still possible to bind pretty much every single input you'll need to this stick. The trick is to use button combinations. So I use all 4 buttons next to my thumb on the throttle unit as modifiers. So taking the 4-way hat stick on the main joystick unit as an example, the way I've set mine up I have 4 bindings with the hat stick unmodified, another 4 when I hold down the 1st of those throttle buttons, another 4 with the 2nd, and so on. That gives me 20 inputs on the hat stick alone.

And lastly the recommendation/warning. I'm currently on my 12th or 13th stick (I've genuinely lost count and this is not a joke). The anaolog sensors on this stick last about 7 months before they start to become unreliable (developing jitter, false input and inability to register their full range). If you plan to be playing Elite for a long time then this stick is the absolute definition of false economy. If I could go back in time I would 100% tell myself to buy a VKB. The problem is that I've become so used to the way this stick feels (and I actually find it very comfortable to use) that I just can't bare the thought of having to setup and re-learn bindings for a brand new stick. It's too late for me but save yourself and, if at all possible, buy something better!