The conditions you mention are not the most harsh possible, but I guess your alcohols are acid-sensitive to some extent.
Especially the tertiary hydroxyls with vicinal protons could suggest a possible dehydration, yielding enols (which would then tautomerize to carbonyl cpds).
If this is the case, of course you can't use bromine water for analysing them. The substitution of OH by Br2 (which I have never heard of, actually) wouldn't be the main issue.
I'm not sure, however, because in fact you can heat solutions of sucrose with aq. acids to get fructose and glucose.
It's probably a matter of concentrations and temperature. You can check previous literature for transformations involving your alcohols, to see if acidic conditions have yet been used.