If I mix an aqueous solution of hydrogen chloride with an organic solvent, will the organic solvent contain hydrogen ions? For example, let's say I mix $36\ \text{cm}^3$ 2-propanol, $9\ \text{cm}^3$ methyl ethyl ketone and $15\ \text{cm}^3$ hydrochloric acid with a concentration of $1,0\ \text{mol}/\text{dm}^3$. 

The hydrochloric acid is solved in water, and since the other compounds are organic and less dense than water they should form two layers. Would the upper layer be "acidic"?

This is an elution I've used in a thin-layer-chromatography lab and I'm trying to figure out what role the hydrochloric acid plays in affecting the compounds' ability to bind to the elution (mobile phase).
$\ce {HCl}$ is so strong a proton donor that bases weaker than water could be protonated.  Alcohols and etherss, if they form a separate phase from water, are likely to be protonated.  Going the other direction, some organic compounds with little solubility in water might become more soluble in a hydrochloric acid solution if they are sufficiently basic.  The basicity of some cyclopropenones can be measured that way.  See (behind a paywall) http://pubs.acs.org/doi/abs/10.1021/cr60288a003?journalCode=chreay.