Yes, your theory is correct. If side chained the gate on Vocal2 will only be open when vocal1 is above the threshold gain.
Explanation of side chaining: http://www.soundonsound.com/sos/nov06/articles/sidechain.htm
Setting up a side chain: http://brianboylemusic.com/2011/05/10/side-chain-compression-explained/
This isn't my genre at all - but I'd say overall the vocals are way too loud & the track constantly ducks behind them… which is entirely the wrong way round.
This type of music is entirely reliant on a solid beat (far too understated in the example given) which the vox ought to stay well out of the way of.
I'd look at the compression chain differently. ...
If you were using either Compressor plug-in built into Ableton, you would be able to select your Drum track in the "Sidechain" panel of the compressor, accessed by pressing the little arrow in the top bar of the plugin. You don't need to use the "Audio to" function at all. I wouldn't be surprised if your VST Compressor has a similar function.
One thing you could do is:
Duplicate the layer you wish to do this on
on one layer EQ everything EXCEPT the frequencies you want to duck
on the other layer ONLY EQ the frequencies you want to duck
side-chain your kick to the second layer (the one with ONLY the frequencies that you want to duck)
Let me know how it goes.