Flip-- here's an expiriment for you to try.. Take some of your HCl and boil it!!! Yes, take a litre, 500ml, whatever.. and boil it!! In your world, where all the hydrogen chloride boils before the water, the pH of the liquid should = 7 LONG before the liquid is removed..
Ok... this is why it's called a solubility curve. As temp increases, gas solubility decreases, but this is not a y = -x type of equation. Eventually, yes, the bp of the water will be reached and the HCl left in solution would come over with it.
However, I indeed have never distilled HBr, and if there is some logical fallacy to my argument then please point it out.
Flip
http://www.chemeng.ed.ac.uk/~neilm/new/azeotope/HH.html#Hydrogen_chloride (http://www.chemeng.ed.ac.uk/~neilm/new/azeotope/HH.html#Hydrogen_chloride)