Sadly, not really. Firstly, the high freqs get additionally damped by a wall if you're in another room, secondly, what you're doing is basically listen to the track at very low volume (hearing threshold) and here comes the human perception into play. Have a look at this graph http://www.sengpielaudio.com/Acoustics226-2003.pdf (if someone has difficulties to read it, the lower a part of a curve is, the more sensitive we are to it).
At very low volume you hear best what's in the 3.5 - 3.8kHz range. So on one hand you're right, you should mostly hear vocs and snare, but you can't make any statement about the level balance of the rest of the frequencies. For this you'll need pretty high listening volume.