I spoke with an organic prof in our department, and she thought the stabilization through resonance would be stronger than the destabilization by the electron withdrawing nature of the halogen. Thus, she thought the alkene would open to put the carbocation on the right. She also thought it was a probably outside the scope of a standard undergrad organic course.
To answer what I think is your main question, if the alkene is disubstituted, and there is no major stabilizing factor on one side (like in the example above), Markovnikov's rule will not predict one regioisomer over the other - you would probably see both regioisomers in about the same yield.